Question 114: Dual Nature of Matter and Radiation

Question

Proton $$(\mathrm{P})$$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $$\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$$ ):

Accepted Answer

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

Answer

1 : 1

Answer

1 : 43

Answer

1 : 1849

Answer

43 : 1

Dual Nature of Matter and Radiation

Proton $(\mathrm{P}) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, \mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$ ):

Choose the correct answer: