JEE MAIN - Physics (2023 - 8th April Morning Shift - No. 17)
Proton $$(\mathrm{P})$$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $$\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$$ ):
1 : 1
1 : 43
1 : 1849
43 : 1
Explanation
The de Broglie wavelength of a particle is given by the formula:
$$\lambda = \frac{h}{p}$$
where $h$ is Planck's constant and $p$ is the momentum of the particle.
If the de Broglie wavelengths of the proton and electron are the same, then:
$$\frac{h}{p_p} = \frac{h}{p_e}$$
where $p_p$ and $p_e$ are the momenta of the proton and electron, respectively.
Solving this equation for the ratio of their momenta gives:
$$\frac{p_p}{p_e} = 1$$
So, the ratio of their momenta is 1:1
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