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The following texts contain pretty much all instances mentioning Nadav and Abihu in the Torah
(א) וַיִּקְח֣וּ בְנֵֽי־אַ֠הֲרֹן נָדָ֨ב וַאֲבִיה֜וּא אִ֣ישׁ מַחְתָּת֗וֹ וַיִּתְּנ֤וּ בָהֵן֙ אֵ֔שׁ וַיָּשִׂ֥ימוּ עָלֶ֖יהָ קְטֹ֑רֶת וַיַּקְרִ֜בוּ לִפְנֵ֤י יְהוָה֙ אֵ֣שׁ זָרָ֔ה אֲשֶׁ֧ר לֹ֦א צִוָּ֖ה אֹתָֽם׃ (ב) וַתֵּ֥צֵא אֵ֛שׁ מִלִּפְנֵ֥י יְהוָ֖ה וַתֹּ֣אכַל אוֹתָ֑ם וַיָּמֻ֖תוּ לִפְנֵ֥י יְהוָֽה׃
(1) Now Aaron’s sons Nadab and Abihu each took his fire pan, put fire in it, and laid incense on it; and they offered before the LORD alien fire, which He had not enjoined upon them. (2) And fire came forth from the LORD and consumed them; thus they died at the instance of the LORD.
(א) וַיְדַבֵּ֤ר יְהוָה֙ אֶל־מֹשֶׁ֔ה אַחֲרֵ֣י מ֔וֹת שְׁנֵ֖י בְּנֵ֣י אַהֲרֹ֑ן בְּקָרְבָתָ֥ם לִפְנֵי־יְהוָ֖ה וַיָּמֻֽתוּ׃
(1) The LORD spoke to Moses after the death of the two sons of Aaron who died when they drew too close to the presence of the LORD.
(ג) וַיֹּ֨אמֶר מֹשֶׁ֜ה אֶֽל־אַהֲרֹ֗ן הוּא֩ אֲשֶׁר־דִּבֶּ֨ר יְהוָ֤ה ׀ לֵאמֹר֙ בִּקְרֹבַ֣י אֶקָּדֵ֔שׁ וְעַל־פְּנֵ֥י כָל־הָעָ֖ם אֶכָּבֵ֑ד וַיִּדֹּ֖ם אַהֲרֹֽן׃ (ד) וַיִּקְרָ֣א מֹשֶׁ֗ה אֶל־מִֽישָׁאֵל֙ וְאֶ֣ל אֶלְצָפָ֔ן בְּנֵ֥י עֻזִּיאֵ֖ל דֹּ֣ד אַהֲרֹ֑ן וַיֹּ֣אמֶר אֲלֵהֶ֗ם קִ֠רְב֞וּ שְׂא֤וּ אֶת־אֲחֵיכֶם֙ מֵאֵ֣ת פְּנֵי־הַקֹּ֔דֶשׁ אֶל־מִח֖וּץ לַֽמַּחֲנֶֽה׃
(3) Then Moses said to Aaron, “This is what the LORD meant when He said: Through those near to Me I show Myself holy, And gain glory before all the people.” And Aaron was silent. (4) Moses called Mishael and Elzaphan, sons of Uzziel the uncle of Aaron, and said to them, “Come forward and carry your kinsmen away from the front of the sanctuary to a place outside the camp.”
(ד) וַיָּ֣מָת נָדָ֣ב וַאֲבִיה֣וּא לִפְנֵ֣י יְהוָ֡ה בְּֽהַקְרִבָם֩ אֵ֨שׁ זָרָ֜ה לִפְנֵ֤י יְהוָה֙ בְּמִדְבַּ֣ר סִינַ֔י וּבָנִ֖ים לֹא־הָי֣וּ לָהֶ֑ם וַיְכַהֵ֤ן אֶלְעָזָר֙ וְאִ֣יתָמָ֔ר עַל־פְּנֵ֖י אַהֲרֹ֥ן אֲבִיהֶֽם׃ (פ)
(4) But Nadab and Abihu died by the will of the LORD, when they offered alien fire before the LORD in the wilderness of Sinai; and they left no sons. So it was Eleazar and Ithamar who served as priests in the lifetime of their father Aaron.
(א) וְאֶל־מֹשֶׁ֨ה אָמַ֜ר עֲלֵ֣ה אֶל־יְהוָ֗ה אַתָּה֙ וְאַהֲרֹן֙ נָדָ֣ב וַאֲבִיה֔וּא וְשִׁבְעִ֖ים מִזִּקְנֵ֣י יִשְׂרָאֵ֑ל וְהִשְׁתַּחֲוִיתֶ֖ם מֵרָחֹֽק׃
(1) Then He said to Moses, “Come up to the LORD, with Aaron, Nadab and Abihu, and seventy elders of Israel, and bow low from afar.
(כב) וַיִּשָּׂ֨א אַהֲרֹ֧ן אֶת־ידו [יָדָ֛יו] אֶל־הָעָ֖ם וַֽיְבָרְכֵ֑ם וַיֵּ֗רֶד מֵעֲשֹׂ֧ת הַֽחַטָּ֛את וְהָעֹלָ֖ה וְהַשְּׁלָמִֽים׃ (כג) וַיָּבֹ֨א מֹשֶׁ֤ה וְאַהֲרֹן֙ אֶל־אֹ֣הֶל מוֹעֵ֔ד וַיֵּ֣צְא֔וּ וַֽיְבָרֲכ֖וּ אֶת־הָעָ֑ם וַיֵּרָ֥א כְבוֹד־יְהוָ֖ה אֶל־כָּל־הָעָֽם׃ (כד) וַתֵּ֤צֵא אֵשׁ֙ מִלִּפְנֵ֣י יְהוָ֔ה וַתֹּ֙אכַל֙ עַל־הַמִּזְבֵּ֔חַ אֶת־הָעֹלָ֖ה וְאֶת־הַחֲלָבִ֑ים וַיַּ֤רְא כָּל־הָעָם֙ וַיָּרֹ֔נּוּ וַֽיִּפְּל֖וּ עַל־פְּנֵיהֶֽם׃

(22) Aaron lifted his hands toward the people and blessed them; and he stepped down after offering the sin offering, the burnt offering, and the offering of well-being. (23) Moses and Aaron then went inside the Tent of Meeting. When they came out, they blessed the people; and the Presence of the LORD appeared to all the people. (24) Fire came forth from before the LORD and consumed the burnt offering and the fat parts on the altar. And all the people saw, and shouted, and fell on their faces.

Here is an article that can be a good guide to explore your topic deeper: https://www.myjewishlearning.com/article/boundaries-sanctity-and-silence/

Boundaries, Sanctity And Silence by Rabbi Cary Kozberg
Although we can attempt to understand the deaths of Nadav and Avihu, we are ultimately limited and often feel powerless in the face of God.
https://www.myjewishlearning.com/article/the-time-and-place-for-spontaneity/

The Time And Place For Spontaneity by Rabbi Shimon Felix
This article looks at the value and danger of spontaneous religious expression
Loads of classical (and not so classical) commentaries here!
(א) ותצא אש. רַ' אֱלִיעֶזֶר אוֹמֵר לֹא מֵתוּ בְנֵי אַהֲרֹן אֶלָּא עַל יְדֵי שֶׁהוֹרוּ הֲלָכָה בִּפְנֵי מֹשֶׁה רַבָּן, רַבִּי יִשְׁמָעֵאל אוֹמֵר שְׁתוּיֵי יַיִן נִכְנְסוּ לַמִּקְדָּשׁ, תֵּדַע, שֶׁאַחַר מִיתָתָן הִזְהִיר הַנּוֹתָרִים שֶׁלֹּא יִכָּנְסוּ שְׁתוּיֵי יַיִן לַמִּקְדָּשׁ, מָשָׁל לְמֶלֶךְ שֶׁהָיָה לוֹ בֶן בַּיִת וְכוּ', כִּדְאִיתָא בְּוַיִּקְרָא רַבָּה: (א) הוא אשר דבר וגו'. הֵיכָן דִּבֵּר? וְנֹעַדְתִּי שָׁמָּה לִבְנֵי יִשְֹרָאֵל וְנִקְדַּשׁ בִּכְבֹדִי (שמות כ"ט), אַל תִּקְרֵי בִּכְבֹדִי אֶלָּא בִּמְכֻבָּדַי; אָמַר לוֹ מֹשֶׁה לְאַהֲרֹן, אַהֲרֹן אָחִי, יוֹדֵעַ הָיִיתִי שֶׁיִּתְקַדֵּשׁ הַבַּיִת בִּמְיֻדָּעָיו שֶׁל מָקוֹם, וְהָיִיתִי סָבוּר אוֹ בִי אוֹ בְךָ, עַכְשָׁיו רוֹאֶה אֲנִי שֶׁהֵם גְּדוֹלִים מִמֶּנִּי וּמִמְּךָ (ספרא):

(1) ותצא אש AND THERE WENT OUT FIRE — Rabbi Eleizer said: the sons of Aaron died only because they gave decisions on religious matters in the presence of their teacher, Moses (Sifra, Shemini, Mechilta d'Miluim 2 32; Eruvin 63a). Rabbi Ishmael said: they died because they entered the Sanctuary intoxicated by wine. You may know that this is so, because after their death he admonished those who survived that they should not enter when intoxicated by wine (vv. 8—9). A parable! It may be compared to a king who had a bosom friend, etc., as is to be found in Leviticus Rabbah 12:1, 4 (cf. Biur). (1) ‎‎ '‏וגו‎‎‎ 'הוא אשר דבר ה‎ THIS IS WHAT THE LORD SPOKE, etc. — Where had He spoken this? In the statement (Exodus 29:43), “And there I will be met by the children of Israel and it (the Tabernacle) shall be sanctified by My glory (בכבודי).” Read not here בִכְבוֹדִי, “by My Glory” but בִּמְכֻבָּדַי, “through My honoured ones” (Zevachim 115b). Moses here said to Aaron: “My brother, Aaron! I knew that this House was to be sanctified by those who are beloved of the Omnipresent God and I thought it would be either through me or through thee; now I see that these (thy sons who have died) are greater than me and than thee!” (Leviticus Rabbah 12 2).

(א) [א] "וידבר ה' אל משה אחרי מות שני בני אהרן" מה תלמוד לומר? לפי שנאמר "ויקחו בני אהרן נדב ואביהוא איש מחתתו" – "בני אהרן" לא נטלו עצה מאהרן, "נדב ואביהוא" לא נטלו עצה ממשה, "איש מחתתו" איש איש מעצמו עשה, לא נטלו עצה זה מזה. מנין שכשם שעבירת שניהם שוה כך מיתת שניהם שוה? ת"ל "אחרי מות שני בני אהרן".

(ב) [ב] "בקרבתם לפני ה' וימותו" – ר' יוסי הגלילי אומר, על הקְריבה מתו ולא מתו על ההקרבה. ר' עקיבא אומר, "בקרבתם לפני ה' וימותו", וכתוב אחד אומר "ויקריבו לפני ה' אש זרה" (ויקרא י)... הכריע "בהקריבם אש זרה לפני ה'" (במדבר ג, במדבר כו) – הוי על ההקרבה מתו ולאמיתו על הקריבה. ר' אלעזר בן עזריה אומר, כדאי הקרבה לעצמה וכדאי קריבה לעצמה.

(1) 1) (Vayikra 16:1) ("And God spoke to Moses after the death of the two sons of Aaron when they drew near before God and they died,") "And God spoke to Moses after the death of the two sons of Aaron": What is the intent of this ("two")? Because it is written (Vayikra 10:1) "And the sons of Aaron took, Nadav and Avihu, each his coal-pan" — "the sons of Aaron" — they did not seek counsel from Aaron; "Nadav and Avihu" — they did not seek counsel from Moses; "each his coal-pan" — each by himself; they did not take counsel from each other. Whence is it derived that just as the transgression of the two was identical, so the death of the two was identical? From "after the death of the two sons of Aaron."

(2) 2) "when they drew near before the L–rd and they died": R. Yossi Haglili says: They died because of the drawing near (and entering the holy of holies without permission), and not because of the incense offering. R. Akiva says: They died because of the offering and not because of the drawing near. One verse (our verse) states "when they drew near before the L–rd and they died," and another verse states (Vayikra 11:1) "and they offered before the L–rd a strange fire." The resolution (Bamidbar 3:4) "when they drew near (with) a strange fire before the L–rd" — They died because of the drawing near and not because of the offering. R. Elazar b. Azaryah says: The offering is sufficient (for death) unto itself, and the drawing near is sufficient unto itself.

וכבר היו משה ואהרן מהלכין בדרך ונדב ואביהוא מהלכין אחריהן וכל ישראל אחריהן אמר לו נדב לאביהוא אימתי ימותו שני זקנים הללו ואני ואתה ננהיג את הדור אמר להן הקב"ה הנראה מי קובר את מי אמר רב פפא היינו דאמרי אינשי נפישי גמלי סבי דטעיני משכי דהוגני

Apropos the deaths of Nadav and Avihu, an aggadic midrash on this subject is quoted: And it had already happened that Moses and Aaron were walking on their way, and Nadav and Avihu were walking behind them, and the entire Jewish people were walking behind them. Nadav said to Avihu: When will it happen that these two old men will die and you and I will lead the generation, as we are their heirs? The Holy One, Blessed be He, said to them: We shall see who buries whom. Rav Pappa says: This explains the adage that people say: Many are the old camels that are loaded with the skins of young camels.

(א) וישימו עליה קטרת. משלהם. היינו ויקריבו לפני ה׳‎ אש זרה שהרי אי אפשר לקטרת בלא אש וכל קטרת שאינה משל צבור נקראת זרה. (ב) אשר לא צוה אתם. פי׳‎ אשר לא לעשות צוה אותם כדכתיב ולא תעלו עליו קטרת זרה דוגמת לשרוף את בניהם ואת בנותיהם אשר לא צויתי אותם.
(1) .וישימו עליה קטורת, “they placed incense on it.” They had taken this from the table. This is what is meant by the line: ויקריבו לפני ה' אש זרה, “they tendered before the Lord alien fire.” Incense without fire is an impossibility. Any incense offering that is not presented in the name of a community is called: “alien.” (2) אשר לא צוה אותם, “which He had not commanded them (to offer)”. The meaning, as opposed to the translation, is: “that He had commanded them not to offer.” Proof of this is tobe found in Exodus 30,9: לא תעלו עליו קטורת זרה, “do not offer alien incense upon it.!” An example of a similar construction is found in Jeremiah 7,31: לשרוף את בניהם ואת בנותיהם באש אשר לא צויתי, “to burn their sons and daughters, which I did not command.”
(א) אחרי מות. אחרי שהזהיר את ישראל שלא ימותו אמר השם למשה שיזהיר גם לאהרן שלא ימות כאשר מתו בניו וזאת הפרשה לאות כי בני אהרן הכניסו הקטורת לפנים מהפרכת:
(1) after the death After warning Israel not to die [15:31], God now tells Moshe to warn Aaron not to die as his two sons died [10:2].
(ה) וע"ד הפשט יראה לי כי הכתוב הזה מבאר שתי עברות שהיו בידם, האחת במחשבה אשר עליה נגזרה עליהם מיתה, והשנית במעשה שמתו בה. חטא המחשבה קרבתם לפני ה' בהר סיני אחר שהתרה משה בהם וממנה נתחייבו מיתה, הוא שדרשו רז"ל (שמות כ״ד:י״א) ואל אצילי בני ישראל לא שלח ידו, מכאן שהיו ראויין לשליחות יד אלא שנצולו לפי שעה כדי שלא לערבב שמחת התורה, וזהו לשון בקרבתם ולא אמר בהקריבם. חטא המעשה שמתו בו, הוא הקרבת אש זרה, כענין שכתוב (ויקרא י׳:א׳) ויקריבו לפני ה' אש זרה, ואש זרה היתה שהכניסו אש בלא קטורת, ויהיה שעור הכתוב אחרי מות שני בני אהרן וימותו, אחר שנגזרה מיתה על שני בני אהרן בחטא המחשבה בקרבתם לפני ה' בהר סיני שזנו עיניהם מהשכינה וימותו באחד בניסן בחטא המעשה בהקרבת אש זרה, אמר הקב"ה למשה בדבור ובאמירה שיאמר לאהרן שיזהיר שלא יבא בכל עת אל הקדש מבית לפרכת אלא בקטרת, כענין שכתוב בפרשה והביא מבית לפרכת ונתן את הקטרת על האש לפני ה' וכסה ענן הקטרת את הכפרת ולא ימות, הא אם נכנס שם בלא קטרת ימות כדרך שמתו בניו.
(5) Looking at the plain meaning of the text I believe that this verse reveals two separate sins these sons of Aaron were guilty of. One sin was of an intellectual nature, i.e. their thinking, their attitude. Death was decreed for them for that sin. This is the meaning of Tanchuma Acharey 6 that the verse in Exodus 24,11 that “G’d did not stretch out His hand against the nobles of Israel who gazed at G’d and ate and drank,” meant that their punishment was placed in abeyance at that time. The words make it plain that these men were already guilty of death at that time. They were temporarily saved as G’d did not want to spoil the joy of the revelation, the giving of the Torah, at that time. This is all derived by inference because in this instance the Torah speaks of בקרבתם instead of בהקריבם. The latter word means: “when they performed an act of offering, etc.” The former word means: “when they came close,” i.e. intellectually. The sin consisting of a deed was the offering of external fire which was not authorised for them to do, (Leviticus 10,1). They offered the fire without offering incense at the same time, seeing mention of their placing incense on their censers appears to refer to a separate action. We may therefore understand the verse in front of us as meaning: “after the death of the two sons of Aaron who had died seeing that G’d had decreed death for them because they were guilty of a sin involving thought when they had come too close before the Lord during the revelation at Mount Sinai feasting their eyes on a vision of G’d.” They died only on the first day of Nissan following (almost 10 months later) because of the additional sin in deed when they introduced external fire as an offering.
When G’d spoke to Moses here He used both the form of address known as אמירה, and that known as דבור. Verse 1 mentions the latter, verse 2 the former kind of address. He was to tell Aaron (אמירה, in a friendly manner) that he and other priests must not enter the part of the Sanctuary which is beyond the dividing curtain except armed with incense. This is elaborated on in verses 12-13 where the Torah describes the cloud of incense covering the lid of the Holy Ark as insurance against Aaron (or whichever High Priest) dying during this procedure. If Aaron were to enter the Holy of Holies without the incense he would die just as his sons had died.