Exams › JEE Main › Physics

Muon (μ⁻) is negatively charged [|q| = |e|] with a mass mμ = 200 me, where me is the mass of the electron and e is the electronic charge. If μ⁻ is bound to a proton to form a hydrogen like atom, identify the correct statements - (a) Radius of the muonic orbit is 200 times smaller than that of the electron (b) the speed of the μ⁻ in the nth orbit is 1/200 times that of the electron in the nth orbit (c) The ionization energy of muonic atom is 200 times more than that of an ordinary atom (d) The momentum of the muon in the nth orbit is 20 times more than that of the electron [JEE-Main On line-2018]

1. (a), (b), (d)
2. (b), (d)
3. (c), (d)
4. (a), (c), (d)

Correct answer: (a), (c), (d)

Solution

The radius of the muonic orbit is smaller due to the muon's greater mass, leading to a radius that is 200 times smaller than that of the electron. The ionization energy is higher because it is inversely proportional to the mass of the orbiting particle, resulting in 200 times more energy for the muon. Additionally, the momentum of the muon is greater due to its mass, making it 20 times more than that of the electron in the same orbit.

Related JEE Main Physics questions

• An electron in one Bohr orbit with principal quantum number $n=n_1$ can produce 3 distinct spectral lines on de-excitation. In another orbit with principal quantum number $n=n_2$, it can produce 6 distinct spectral lines. What is the ratio of the orbital speeds of the electron in these two orbits?
• An electron in a hydrogen atom is found in an excited state with energy equal to $-3.4$ eV. What is its angular momentum?
• A beam of electrons having energy 12.5 eV is directed at hydrogen gas in the gaseous state at room temperature. The emitted spectrum will contain:
• A hydrogen atom and a $\text{Li}^{2+}$ ion are each in their second excited state. If their electronic angular momenta are denoted by $L_H$ and $L_{Li}$, and their energies by $E_H$ and $E_{Li}$ respectively, which statement is correct?
• For a proton–electron system, the interaction potential is $V = V_0 \ln(r/r_0)$, where $r_0$ is a constant. If Bohr’s model is assumed to hold, how does the radius $r_n$ depend on the principal quantum number $n$?
• In the hydrogen spectrum, the longest wavelength in the ultraviolet region is 122 nm. The shortest wavelength in the infrared region, rounded to the nearest whole number, is

⚔️ Practice JEE Main Physics free + battle 1v1 →