KEAM 2014 Physics and Chemistry Paper

Given,
me= mass of the electron
mp= mass of proton
By de-Broglie wavelength of matter waves
λ=‌

h

p

 (∵p=mv)
∴λ=‌

h

mv

If K be the kinetic energy of the electron, then
K=‌

1

2

mv2 or v=√2K∕m
Now, λ=‌

h

m√2K/m

λ=‌

h

√2Km

So, λ∝‌

1

√m

λe=‌

1

√me

....(i)
λp=‌

1

√mp

.....(ii)
From Eqs. (i) and (ii), we get
‌

λe

λp

=‌

1/√me

1/√mp

‌

λe

λp

=√‌

mp

me