The two particles A and B have de-Broglie wavelength 1 nm and 5 nm respectively. If mass of A is four times the mass of the B, the ratio of kinetic energies of A and B would be

Question

The two particles A and B have de-Broglie wavelength 1 nm and 5 nm respectively. If mass of A is four times the mass of the B, the ratio of kinetic energies of A and B would be (A) 5: 1 (B) 25: 4 (C) 20: 1 (D) 5: 4

Tardigrade Admin · Accepted Answer

(λA/λB) = √(mAEA/mBEB) ∴ (EA/EB) = [(λB/λA)]2 (mB/mA) =((5/1))2× (1/4) = (25/4)

Q. The two particles A and B have de-Broglie wavelength $1 nm$ and $5 nm$ respectively. If mass of A is four times the mass of the B, the ratio of kinetic energies of A and B would be

5 : 1

25 : 4

20 : 1

5 : 4

$\frac{λ _{A}}{λ _{B}} = \frac{m _{A} E _{A}}{m _{B} E _{B}}$
$∴ \frac{E _{A}}{E _{B}} = [\frac{λ _{B}}{λ _{A}}]^{2} \frac{m _{B}}{m _{A}}$
$= (\frac{5}{1})^{2} \times \frac{1}{4} = \frac{25}{4}$

Q. The two particles A and B have de-Broglie wavelength 1nm and 5nm respectively. If mass of A is four times the mass of the B, the ratio of kinetic energies of A and B would be