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

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 Planck's 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 wavelength of particle be x. Velocity, v =(x/100) ∵ λ =(h/m v) ∴ x =(h × 100/m × x) x2 =100 (h/m) x =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 Planck's constant $(h)$ is

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

$10 \frac{h}{m}$

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

$10 \frac{m}{h}$

Let wavelength of particle be $x$ .
Velocity, $v = \frac{x}{100}$
$∵ λ = \frac{h}{m v}$
$∴ x = \frac{h \times 100}{m \times x}$
$x^{2} = 100 \frac{h}{m}$
$x = 10 \frac{h}{m}$

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 Planck's constant (h) is

101​hm​​

10mh​​

101​mh​​

10hm​​