Atomic Structure | Physics JEE previous year questions with Solutions

Q 11 :
In an alpha particle scattering experiment distance of closest approach for the $α$ particle is $4.5 \times 10^{- 14} m$ . If target nucleus has atomic number 80, then maximum velocity of $α$ -particle is ________ $\times 10^{5}$ m/s approximately.

$(\frac{1}{4 π ε_{0}} = 9 \times 10^{9}$ SI unit, mass of $α$ particle = $6.72 \times 10^{- 27}$ kg $)$ [2024]

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(156) $\frac{K Q q}{r_{\min}} = \frac{1}{2} m v^{2} \Rightarrow v = \sqrt{\frac{2 K (Z e) \cdot (2 e) q}{m r_{\min}}} = \sqrt{\frac{4 K Z e^{2}}{m r_{\min}}}$

$\Rightarrow v = \sqrt{\frac{4 \times 9 \times 10^{9} \times 80 \times {(1.6 \times 10^{- 19})}^{2}}{6.72 \times 10^{- 27} \times 4.5 \times 10^{- 14}}}$

$= 1.56 \times 10^{7} m / s = 156 \times 10^{5} m / s$

Q 12 :
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

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(144) Longest wavelength corresponds to transition between $n = 3$ and $n = 4$

$\frac{1}{λ} = R Z^{2} (\frac{1}{3^{2}} - \frac{1}{4^{2}}) = R Z^{2} (\frac{1}{9} - \frac{1}{16}) = \frac{7 R Z^{2}}{9 \times 16}$

$\Rightarrow λ = \frac{144}{7 R}$ for $Z = 1$

$∴ α = 144$

Q 13 :
A electron of hydrogen atom in an excited state is having energy $E_{n} = - 0.85$ $e V$ . The maximum number of allowed transitions to lower energy level is ______ . [2024]

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(6) $E_{n} = - \frac{13.6}{n^{2}} = - 0.85 \Rightarrow n = 4$

$Number of transitions = \frac{n (n - 1)}{2} = \frac{4 (4 - 1)}{2} = 6$

Topic Question Set

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Q 12 :
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

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Q 13 :
A electron of hydrogen atom in an excited state is having energy $E_{n} = - 0.85$ $e V$ . The maximum number of allowed transitions to lower energy level is ______ . [2024]

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Topic Question Set

Q 11 : In an alpha particle scattering experiment distance of closest approach for the α particle is 4.5×10-14m. If target nucleus has atomic number 80, then maximum velocity of α-particle is ________ ×105m/s approximately. (14πε0=9×109 SI unit, mass of α particle = 6.72×10-27 kg) [2024]

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Q 12 : If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be α7R, where α = _______ . [2024]

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Q 13 : A electron of hydrogen atom in an excited state is having energy En=-0.85 eV. The maximum number of allowed transitions to lower energy level is ______ . [2024]

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Q 12 :
If Rydberg's constant is R, the longest wavelength of radiation in Paschen series will be $\frac{α}{7 R}$ , where $α$ = _______ . [2024]

Q 13 :
A electron of hydrogen atom in an excited state is having energy $E_{n} = - 0.85$ $e V$ . The maximum number of allowed transitions to lower energy level is ______ . [2024]