Q24 / 104 · NTA Abhyas (JEE Main) 2020 · Physics · Atomic Physics

For sodium light, the two yellow lines occur at λ1 and λ2 wavelengths. If the mean of these two is 6000 A∘ and λ2-λ1=6 A∘, then the approximate energy difference between the two levels corresponding to λ1 and λ2 is

  • Correct answer
    A
    2×10-3 eV
  • B
    2 eV
  • C
    2000 eV
  • D
    2×10-6 eV

Solution

Given, mean of λ1 and λ2=6000 Å

λ2-λ1=6 Å

i.e. λ1+λ22=6000 Å

λ1+λ2=12000 Å ...(i)

λ2-λ1=6 Å ...(ii)

Equating Equation (i) and (ii), we get

2λ1=12006

λ2=120062=6003 Å

and λ1=5997 Å

Now, the energy difference is

∆E=hcλ1-hcλ2

∆E=hc1λ1-1λ2

∆E=6.6×10-34×3×108×λ2-λ1λ1λ2

=6.6×10-34×3×108×6×10-105997×10-10×6003×10-10×1.6×10-19 eV 

=2.12×10-3 eV≃2×10-3 eV

Hence, the correct answer is option: 'A'.

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