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Question

# The potential energy of a particle of mass m is given by, U(x)={E0;0≤x≤10;x>1 λ1 and λ2 are the de-Broglie wavelengths of the particle, when 0≤x≤1 and x>1 respectively. If the total energy of particle is 2E0, then ratio λ1λ2 will be

A
2
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B
1
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C
2
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D
12
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Solution

## The correct option is C √2Given, Total Energy=2E0 For, (0≤x≤1)→ P.E=E0 K.E=2E0−E0=E0 ⇒λ1=h√2mE0 For, (x>1)→ P.E=0 K.E=2E0 ⇒λ2=h√4mE0 ⇒λ1λ2=√2 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (C) is the correct answer.

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