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A photon of wavelength λ is absorbed by an electron confined to a box of length 35 h λ 8 m c . As a result, the electron makes a transition from state, k = 1 to the state n . Subsequently, the electron transits from the state n to the state m by emitting a photon of wavelength, λ ' = 1 . 75 λ . Then,

Options

  1. An = 4 ;   m = 2
  2. Bn = 5 ;  m = 3
  3. Cn = 6 ;   m = 4
  4. Dn = 3 ;   m = 1

Correct answer

C. n = 6 ;   m = 4

Step-by-step solution

Let the length of confined box be, l = 35 h λ 8 m c . Kinetic energy of electron after absorbing photon, K = h c λ . The de-Broglie wavelength of electron with this kinetic energy is given as, λ de   Broglie = h 2 m K = h 2 m h c λ = h λ 2 m c . Now, number of loops formed in the confined length is given as, p = l λ d e   B r o g l i e 2 = 2 l λ d e   B r o g l i e ⇒   p = 2 × 35 h λ 8 m c h λ 2 m c = 35 ≈ 6 Electron forms n loops in

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