Question

${\huge{\tt{\orange{\fcolorbox{ref}{blue}{\underline{QUESTION :}}}}}}$

The longest wavelength doublet absorption transition is observed at 589 to 58.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

Tʜɪꜱ Qᴜᴇꜱᴛɪᴏɴ Iꜱ Oɴʟʏ Fᴏʀ Mᴏᴅᴇʀᴀᴛᴏʀꜱ, Bʀᴀɪɴʟʏ Sᴛᴀʀꜱ Aɴᴅ Oᴛʜᴇʀ Bᴇꜱᴛ Uꜱᴇʀꜱ​

Answer 1

Answer

The frequency of first transition is

ν

1

=

λ

1

c

=

589×10

−9

3.0×10

8

=5.093×10

14

s

−1

.

The frequency of second transition is

ν

2

=

λ

2

c

=

589.6×10

−9

3.0×10

8

=5.088×10

14

s

−1

.

The energy difference between two transitions is

ΔE=h(ν

2

−ν

1

)

=6.626×10

−34

×(5.093−5.088)×10

14

=3.313×10

−22

J.

Answer 2

Correct Question:

The longest wavelength doublet absorption transition is observed at 589 to 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

Answer:

• Frequencies: 5.1 × 10¹⁴, 5.08×10¹⁴
• Energy difference = 3.8 × 10⁻²²

For the wavelength of 589 nm,

We know that:

$\bf{c = \lambda \times \nu}$

$\implies \sf{ \nu = \dfrac{c}{ \lambda} }$

where:

• c is the velocity of light
• λ is the wavelength
• ν is the frequency

So,

$\sf{ \nu _{1} = \dfrac{3 \times {10}^{8} }{589 \times {10}^{ - 9} } }$

$\implies \boxed{ \sf{ \nu _{1} = 5.1 \times {10}^{14} }}$

For the wavelength of 589.6 nm,

$\sf{ \nu _{2} = \dfrac{c}{ \lambda} }$

$\implies \sf{ \nu_{2} = \dfrac{3 \times {10}^{8} }{ 589.6 \times {10}^{ - 9} } }$

$\implies \boxed{ \sf{ \nu_{2} = 5.08 \times {10}^{14}} }$

Now, let's find the energy difference between 2 excited states.

$\bf{E = \dfrac{hc}{ \lambda} }$

where:

• h is the Plancks constant = 6.626 × 10⁻³⁴
• E is the energy

$\implies \sf{E_{1} = \dfrac{6.626 \times {10}^{ - 34} \times 3 \times {10}^{8} }{5.89 \times {10}^{ - 9} } }$

$\implies \sf{E_{1} = \dfrac{19.878 \times {10}^{ - 26} }{589 \times {10}^{ - 9} } }$

$\implies \boxed{ \sf{E _{1} = 3.3748 \times {10}^{ - 19} } }$

Similarly,

$\sf{E_{2} = \dfrac{hc}{ \lambda} }$

$\implies \sf{E_2 = \dfrac{19.878 \times {10}^{ - 36} }{589.6 \times {10}^{ - 9} } }$

$\implies \boxed{ \sf{E_2 = 3.371 \times {10}^{ - 19} }}$

Now difference between two energy levels;

$\sf{E_1 - E_2 = {10}^{ - 19} \{3.3748 - 3.371 \}}$

$\therefore \boxed{ \bf{Energy \: difference = 3.8 \times {10}^{ - 22} }}$