The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)

Question

The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)

Smart Achievers · Accepted Answer

(2)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m \cdot K E}}$

$\frac{λ_{d}}{λ_{α}} = \sqrt{\frac{m_{α} \cdot K E_{α}}{m_{d} \cdot K E_{d}}} = \sqrt{\frac{4 m \cdot 2 E}{2 m \cdot E}} = 2 : 1$

Solution

Q.
The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)

Ans.
(2)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m \cdot K E}}$

$\frac{λ_{d}}{λ_{α}} = \sqrt{\frac{m_{α} \cdot K E_{α}}{m_{d} \cdot K E_{d}}} = \sqrt{\frac{4 m \cdot 2 E}{2 m \cdot E}} = 2 : 1$

Want Us to Email you About Special Offers & Updates?

Solution

Q. The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is n:1. The value of n is ____. [2026] (Assume mass of proton = mass of neutron.)

Ans. (2) λ=hmv=h2m·KE λdλα=mα·KEαmd·KEd=4m·2E2m·E=2:1

Want Us to Email you About Special Offers & Updates?

Q.
The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)

Ans.
(2)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m \cdot K E}}$

$\frac{λ_{d}}{λ_{α}} = \sqrt{\frac{m_{α} \cdot K E_{α}}{m_{d} \cdot K E_{d}}} = \sqrt{\frac{4 m \cdot 2 E}{2 m \cdot E}} = 2 : 1$