KVPY SX SB Exam 2016 Question Paper

Question : 94 of 120

Marks: +1, -0

A photon of wavelength λ is absorbed by an electron confined to a box of length

√{{35hλ }/{8mc }}

. 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' = 1.85 λ

. Then

n = 4; m = 2
n = 5; m = 3
n = 6; m = 4
n = 3; m = 1

Validate

Solution:

KE of

e^{–}={hc}/λ

\λ_{\de-\broglie}=h/√{2mKE}

=h/√{2m×{hc}/λ}

=√{hλ}/√{2mc}

{m_0\λ_{\debroglie}}/2=l

m_0/2×√{hλ}/√{2mc}=√{35hλ}/√{8mc}

⇒m_0/{2√2}=√35/{2√2}

m_0=√35=5.8 ≈6

i.e.

e^{–}

get excite to state 6.
∴ n = 6

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