SATHEE: atoms Question 22

atoms Question 22

Question: Q. 16. (i) If electron in the atom is replaced by a particle (muon) having the same charge but mass about 200 times as that of the electron to form amuonic atom, how would : (i) the radius and (ii) the ground state energy of this be affected?

(ii) Calculate the wavelength of the first spectral line in the corresponding Lyman series of this atom.

A [Delhi Comptt. I, II, III 2012]

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Solution:

Ans. (i) Charged muon of mass about $200 m_{e}$ , revolves around a proton.

In Bohr’s atomic model

$\begin{aligned} \propto \frac{1}{m} & So, & \frac{r_{μ}}{r_{e}} & = \frac{m_{e}}{m_{μ}} & or & \frac{r_{μ}}{r_{e}} & = \frac{1}{200} & or & 200 r_{μ} & = r_{e} & or & r_{μ} & = \frac{r_{e}}{200} \end{aligned}$

i.e., the radius reduces to $\frac{1}{200}$ times.

Again, in Bohr’s atomic model

$\frac{E_{μ}}{E_{e}} = \frac{m_{μ}}{m_{e}} = \frac{200}{1}$

$E_{μ} = 200 E_{e}$

i.e. the ground state energy increases by 200

times.

(ii) Eor first spectral line of Lyman series,

$n_{1} = 1, n_{2} = 2$

Difference of energy of electron in hydrogen atom when $n_{1} = 1$ & $n_{2} = 2$

$(Lyman Series) = 10.2 eV$

Hence, for muonic atom this energy

$\begin{aligned} = 10.2 \times 200 eV E & = \frac{12375}{λ (in \AA)} (in eV) So, λ & = \frac{12375}{10.2 \times 200 eV} \AA & = 6.1 \AA & = 0.61 nm \end{aligned}$

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Atoms

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Engineering Preparation

Medical Preparation

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