Physics, asked by gameanandgamepoxh7hu, 1 year ago

An electron and proton are moving in same direction and possess same kinetic energy.find the ratio of de broglie wavelength

Answers

Answered by abhi178
20
electron and proton have same kinetic energy, 
Let kinetic energy = E 
we know,
  kinetic energy = p^2/2m (where p is momentum)
  so, p=(2Em)^1/2 
p =\sqrt{2Em}} 
 for electron,
p_e = \sqrt{2E.m_e}}
and for proton,
p_p=\sqrt{2E.m_p}}
 now use De-broglie equation,
     λ =h/p
so,λe/λp = \frac{p_p}{p_e}
        
=\sqrt{\frac{2E.m_p}{2E.m_e}
we know, 
  m_p=1837m_e
use this above,
λe/λp =√(1837me/me) = √1837
Answered by JunaidMirza
17
Relation between kinetic energy and momentum is
K.E = p² / (2m)

For same kinetic energy
p ∝ √m
p₂ / p₁ = √(m₂ / m₁) ………[1]

De-broglie wavelength (λ) is given as
λ = h / p

λ₁ / λ₂ = p₂ / p₁
= √(m₂ / m₁) …………[∵ From Equation (1)]
= √[1.67 × 10⁻²⁷ kg / (9.1 × 10⁻³¹ kg)]
= 42.83

Ratio of their de-broglie wavelength is 42.83 : 1 (or) 4283 : 100
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