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 Plants constant (h) is

Question

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 Plants constant (h) is (A)  (1/10)√m/h  (B)  10√h/m  (C)  (1/10)√h/m  (D)  10√m/h

Tardigrade Admin · Accepted Answer

Let the velocity of the particle =v ∴ Wavelength (λ ) of the particle =100 v or v=(λ /100) de-Broglie relationship is λ =(h/m.v) λ =(h× 100/m.λ ) or λ 2=(h× 100/m) λ =10√(h/m)

Q. 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 Plants constant $(h)$ is

$\frac{1}{10} m / h$

$10 h / m$

$\frac{1}{10} h / m$

$10 m / h$

Let the velocity of the particle $= v$
$∴$ Wavelength $(λ)$ of the particle
$= 100 v$ or $v = \frac{λ}{100}$
de-Broglie relationship is $λ = \frac{h}{m . v}$
$λ = \frac{h \times 100}{m . λ}$
or $λ^{2} = \frac{h \times 100}{m}$
$λ = 10 \frac{h}{m}$

Q. 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 Plants constant (h) is

101​m/h​

10h/m​

101​h/m​

10m/h​