Question

Calculate the spin magnetic moment and predict magnetic behaviour of Cobalt
(Z=27).

Answer 1

ANSWER:

• The spin magnetic moment of Cobalt = 3.87 BM.

• Magnetic behaviour of Cobalt = Paramagnetic.

GIVEN:

• Z = 27 for Cobalt.

TO FIND:

• The spin magnetic moment of Cobalt.

TO PREDICT:

• Magnetic behaviour of Cobalt

EXPLANATION:

Cobalt electronic configuration : [ Ar ] 4s² 3d⁷

$\setlength{\unitlength}{1 cm} \begin{picture}(0,0)\put(2.2,0.5){ \boldsymbol {3d^7} }\put(0.1,0.5){ \boldsymbol {4s^2} }\put(0,0){ \boxed{\upharpoonleft \downharpoonright} } \put(1,0){ \boxed{\upharpoonleft \downharpoonright}\boxed{\upharpoonleft \downharpoonright}\boxed{\upharpoonleft \ }\boxed{\upharpoonleft \ }\boxed{ \upharpoonleft \ } } \end{picture}$

$\bigstar \ \boxed{ \bold{ \large{ \red{\mu = \sqrt{n(n+2)}}}}}$

$\star \ \sf n \implies No.\ of\ unpaired\ electrons$

$\star \ \textsf{n = 3 (From the electonic configuration)}$

$\sf \longmapsto \mu = \sqrt{3(3+2)}$

$\sf \longmapsto \mu = \sqrt{3(5)}$

$\sf \longmapsto \mu = \sqrt{15}$

$\sf \longmapsto \mu = 3.87 \ BM$

$\bigstar \ \boxed{ \bold{ \blue{Magnetic\ Behaviour = Paramagnetic}}}$

REASON:

• As Cobalt consists of three unpaired electrons it exhibits paramagnetic character.

Answer 2

$\huge\red{\underline{{\bf A}}}$$\huge\pink{\underline{{\bf N}}}$$\huge\green{\underline{{\bf S}}}$$\huge\purple{\underline{{\bf W}}}$$\huge\orange{\underline{{\bf E}}}$$\huge\blue{\underline{{\bf R}}}$

ᴀᴄᴛᴜᴀʟʟʏ,ᴍᴀɢɴᴇᴛɪᴄ ᴍᴏᴍᴇɴᴛ ᴏғ ᴄᴏ3+ ɪs 4.87. ᴛʜɪs ɪs ʜᴏᴡ ɪᴛ ɪs :

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ғᴏʀ ᴍᴀɢɴᴇᴛɪᴄ ᴍᴏᴍᴇɴᴛ,

μ(ᴍᴀɢɴᴇᴛɪᴄ ᴍᴏᴍᴇɴᴛ) = √[ɴ(ɴ+2)]

ᴡʜᴇʀᴇ ɴ ɪs ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴜɴᴘᴀɪʀᴇᴅ ᴇʟᴇᴄᴛʀᴏɴs.

ɴᴏᴡ ɪғ ʏᴏᴜ ᴏʙsᴇʀᴠᴇ, ᴄᴏ3+ ᴄᴏɴғɪɢᴜʀᴀᴛɪᴏɴ ᴡɪʟʟ ʙᴇ

1s2 2s2 2ᴘ6 3s2 3ᴘ6 3ᴅ6 4s0,

ᴀs ᴛʜᴇ ᴇᴍᴘᴛʏ 4s sʜᴇʟʟ ɪs ᴏғ ʟᴏᴡᴇʀ ᴇɴᴇʀɢʏ ᴛʜᴀɴ ᴛʜᴇ ᴇᴍᴘᴛʏ 3ᴅ sʜᴇʟʟ sᴏ ғɪʟʟs ғɪʀsᴛ. ᴏɴᴄᴇ ғᴜʟʟ ɪᴛ ɪs ᴏғ ʜɪɢʜᴇʀ ᴇɴᴇʀɢʏ ᴛʜᴀɴ ᴛʜᴇ 3ᴅ.

ᴄᴏ3+ ᴍᴇᴀɴs ɪᴛ ᴅᴏɴᴀᴛᴇs ᴛᴡᴏ ᴇʟᴇᴄᴛʀᴏɴs ᴀɴᴅ ɴᴏᴡ ɪᴛ ʜᴀs 24 ᴇʟᴇᴄᴛʀᴏɴs.

ɴᴏᴡ, ɪɴ ‘3ᴅ’ ᴏʀʙɪᴛᴀʟ, ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ғʀᴇᴇ ᴇʟᴇᴄᴛʀᴏɴs ᴡᴏᴜʟᴅ ʙᴇ 4 …(ᴀs ‘ᴅ’ ᴏʀʙɪᴛᴀʟ ʜᴀs ᴍᴀxɪᴍᴜᴍ ᴏғ 10 ᴇʟᴇᴄᴛʀᴏɴs.) ɪ.ᴇ. ɴ=4

ʜᴇɴᴄᴇ ʙʏ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ,

μ=√[4(4+2)]

μ=√[4x6] = √24 = 4.89

ɪғ ᴡᴇ ᴛᴀʟᴋ ᴀʙᴏᴜᴛ ᴄᴏ2+, ɴ=3 (ᴄᴏɴғɪɢᴜʀᴀᴛɪᴏɴ : 1s2 2s2 2ᴘ6 3s2 3ᴘ6 3ᴅ7 4s0)

μ=√[3(3+2)]

μ=√[3x5] = μ=√15 = 3.87

sᴏ ᴍᴀɢɴᴇᴛɪᴄ ᴍᴏᴍᴇɴᴛ ᴏғ ᴄᴏ3+ ɪs 4.89 ᴀɴᴅ ᴍᴀɢɴᴇᴛɪᴄ ᴍᴏᴍᴇɴᴛ ᴏғ ᴄᴏ2+ ɪs 3.87.

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