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If the de-Broglie wavelength of a particle of mass m is 100 times its velocity than its value in terms of its mass (m) and Plank’s constant (h) is:
A. 110mh
B. 10hm
C.110hm
D. 10mh

Answer
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Hint: We can use the de-Broglie equation which represents the relation between wavelength, mass of the particle, velocity of the particle and Plank’s constant. Firstly write the equation of the planck and then put the given value to ultimately find the required relation.

Complete step by step solution:
The waves have a dual nature. In 1924 De-Broglie told that the matter also has dual nature. The matter that has linear momentum also has a wave associated with it. The De-Broglie equation gives the relation between wave nature and particle nature. From the known wavelength its mass can be determined and from the given mass the wavelength can be determined.
De-Broglie equation is represented as follows:
λ=hmv
λ is the de-Broglie wavelength of the particle.
his the Planck's constant.
mis the mass of the particle.
v is the velocity of the particle.
It is given that wavelength is 100times its velocity so,
λ=100v
On rearranging for vwe get,
v=λ100
On substituting the value of vin De-Broglie equation we get,
λ=hmλ100
λ=100hmλ
λ2=100hm
λ=10hm
So, the wavelength in terms of its mass (m) and Plank’s constant (h) is 10hm.

Therefore, option (B) 10hm, is correct.

Note: The product of mass and velocity is given as momentum.so, the De-Broglie equation also written as λ=hp where, p is the momentum. The de-Broglie wavelength of the particle is inversely proportional to its momentum. The unit of wavelength is meter. The unit of velocity is meter/second. The value of Planck's constant is 6.6×1034Js.
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