If the de-Broglie wavelength of a particle of mass m is 100 times its velocity then its value in terms of its mass (m) and Planck's constant (h) is

Options

A. `(1)/(10) sqrt((m)/(h))`
B. `10 sqrt((h)/(m))`
C. `(1)/(10) sqrt((h)/(m))`
D. `10 sqrt((m)/(h))`

Answer

B

Explanation

Suppose velocity `(v) = x`
Then de Broglie wavelength `(lamda) = 100x`
Now, `lamda =(h)/(mv) " " :.100x = (h)/(mx)`
or `x^(2) = (1)/(100) (h)/(m) or x = (1)/(10) sqrt((h)/(m))`
Hence, `lamda = 100x = 10 sqrt((h)/(m))`