𝐒𝐂𝐈𝐄𝐍𝐂𝐄 𝐒𝐏𝐄𝐂𝐓𝐑𝐔𝐌
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Let f(x) = x^2+4x +1 , Thus the graph of f is obtained by shifting the graph of:
If each element in the domain of a function has a distinct image in the co-domain, then the function is said to be
Determine the domain and range of the relation with ordered pairs (−1, 4),
(0, 7), (2, 3), (3, 3), (4, −2).
ℙ𝕝𝕒𝕟𝕔𝕜'𝕤 ℚ𝕦𝕒𝕟𝕥𝕦𝕞 𝕋𝕙𝕖𝕠𝕣𝕪
--------------------------------------
❖ Substances that absorb or emit light discontinuously in the form of small packets or bundles.
❖ The smallest packet of energy is called quantum (plural quanta).
❖ The radiation is propagated in the form of waves.
❖ The energy of a quantum is directly proportional to the frequency of the radiation
E ∝ v
E = hv
E = (hc)/ λ =hc v
Where E = Energy of radiation
h = Planck's constant
= 6.626 * 10^-27 * erg .sec
= 6.626 * 10^-34 Joule.sec
❖ A body that can absorb or emit energy in whole number multiple of quantum.
E = nhv
Where n = 1, 2, 3, 4
❖ The frequency of emitted radiation goes from lower to higher as the temperature increases.
𝗝𝗼𝗶𝗻 𝘂𝘀 𝗳𝗼𝗿 𝗺𝗼𝗿𝗲.
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▎𝐐𝐮𝐚𝐧𝐭𝐮𝐦 𝐍𝐮𝐦𝐛𝐞𝐫𝐬 𝐎𝐯𝐞𝐫𝐯𝐢𝐞𝐰
1. 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑁𝑢𝑚𝑏𝑒𝑟 𝑛
• 𝑉𝑎𝑙𝑢𝑒𝑠: 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠 (𝑛 = 1, 2, 3, ...)
• 𝐾𝑒𝑦 𝑃𝑜𝑖𝑛𝑡𝑠:
• 𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑠 𝑠𝑖𝑧𝑒 𝑎𝑛𝑑 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑛𝑢𝑐𝑙𝑒𝑢𝑠.
• 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑠 𝑒𝑛𝑒𝑟𝑔𝑦 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑟𝑏𝑖𝑡𝑎𝑙.
• 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑖𝑛 𝑎 𝑠ℎ𝑒𝑙𝑙: 𝐹𝑜𝑟𝑚𝑢𝑙𝑎: 2𝑛².
• 𝑇𝑟𝑖𝑐𝑘: 𝑅𝑒𝑚𝑒𝑚𝑏𝑒𝑟 "𝑛 𝑖𝑠 𝑓𝑜𝑟 𝑛𝑢𝑚𝑏𝑒𝑟" (1, 2, 3...).
2. 𝐴𝑧𝑖𝑚𝑢𝑡ℎ𝑎𝑙 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑁𝑢𝑚𝑏𝑒𝑟 𝑙
• 𝑉𝑎𝑙𝑢𝑒𝑠: 𝐼𝑛𝑡𝑒𝑔𝑒𝑟𝑠 𝑓𝑟𝑜𝑚 0 𝑡𝑜 (𝑛 - 1).
• 𝐾𝑒𝑦 𝑃𝑜𝑖𝑛𝑡𝑠:
• 𝑅𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑠𝑢𝑏𝑠ℎ𝑒𝑙𝑙𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑎 𝑠ℎ𝑒𝑙𝑙.
• 𝐷𝑒𝑠𝑐𝑟𝑖𝑏𝑒𝑠 𝑠ℎ𝑎𝑝𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑟𝑏𝑖𝑡𝑎𝑙 (𝑠, 𝑝, 𝑑, 𝑓).
• 𝑇𝑟𝑖𝑐𝑘: 𝑇ℎ𝑖𝑛𝑘 "𝑙 𝑖𝑠 𝑓𝑜𝑟 𝑠ℎ𝑎𝑝𝑒" (0=𝑠, 1=𝑝, 2=𝑑, 3=𝑓).
3. 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑁𝑢𝑚𝑏𝑒𝑟 (𝑚𝑙)
• 𝑉𝑎𝑙𝑢𝑒𝑠: 𝐼𝑛𝑡𝑒𝑔𝑒𝑟𝑠 𝑓𝑟𝑜𝑚 –𝑙 𝑡𝑜 +𝑙.
• 𝐾𝑒𝑦 𝑃𝑜𝑖𝑛𝑡𝑠:
• 𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑠 𝑜𝑟𝑖𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑟𝑏𝑖𝑡𝑎𝑙 𝑖𝑛 𝑠𝑝𝑎𝑐𝑒.
• 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑟𝑏𝑖𝑡𝑎𝑙𝑠 𝑓𝑜𝑟 𝑎 𝑔𝑖𝑣𝑒𝑛 𝑙: 𝐹𝑜𝑟𝑚𝑢𝑙𝑎: 2𝑙 + 1.
• 𝑇𝑟𝑖𝑐𝑘: "𝑚 𝑓𝑜𝑟 𝑚𝑎𝑛𝑦 𝑜𝑟𝑖𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛𝑠" (𝑐𝑜𝑢𝑛𝑡 𝑓𝑟𝑜𝑚 -𝑙 𝑡𝑜 +𝑙).
4. 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑆𝑝𝑖𝑛 𝑄𝑢𝑎𝑛𝑡𝑢𝑚 𝑁𝑢𝑚𝑏𝑒𝑟 (𝑚𝑠)
• 𝑉𝑎𝑙𝑢𝑒𝑠: +½ (↑) 𝑜𝑟 -½ (↓).
• 𝐾𝑒𝑦 𝑃𝑜𝑖𝑛𝑡𝑠:
• 𝑅𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 𝑠𝑝𝑖𝑛 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛.
• 𝑇𝑟𝑖𝑐𝑘: "𝑆𝑝𝑖𝑛 𝑢𝑝 𝑜𝑟 𝑠𝑝𝑖𝑛 𝑑𝑜𝑤𝑛" ℎ𝑒𝑙𝑝𝑠 𝑟𝑒𝑐𝑎𝑙𝑙 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑣𝑎𝑙𝑢𝑒𝑠.
▎𝑆𝑢𝑚𝑚𝑎𝑟𝑦 𝑇𝑟𝑖𝑐𝑘
• 𝑀𝑛𝑒𝑚𝑜𝑛𝑖𝑐 𝑓𝑜𝑟 𝑂𝑟𝑑𝑒𝑟: 𝑃𝐴𝑀-𝐸 (𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑎𝑙, 𝐴𝑧𝑖𝑚𝑢𝑡ℎ𝑎𝑙, 𝑀𝑎𝑔𝑛𝑒𝑡𝑖𝑐, 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑆𝑝𝑖𝑛).
𝗝𝗼𝗶𝗻 𝘂𝘀 𝗳𝗼𝗿 𝗺𝗼𝗿𝗲.
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ʏᴏᴜʀ ᴘᴀᴛʜ ᴡᴀʏ ᴛᴏ sᴜᴄᴄᴇss !
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