Atoms & Nuclei

JEE Main level, single correct, medium

148 of 239

Question 148 of 239

Hydrogen (1H1), Deuterium (1H2), singly ionised Helium (2He4)+ and doubly ionised lithium (3Li6)++ all have one electron around the nucleus. Consider an electron transition from n=2n=2 to n=1n=1. If the wave lengths of emitted radiation are λ1,λ2,λ3{\lambda }_{1}\text{,}{\lambda }_{2}\text{,}{\lambda }_{3} and λ4{\lambda }_{4} respectively then approximately which one of the following is correct ?

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Answer: (C) λ1=λ2=4λ3=9λ4{\lambda }_{1}={\lambda }_{2}=4{\lambda }_{3}={9\lambda }_{4}

For radiation, we know that

1λ=RZ2(1n12−1n22)\dfrac{1}{\lambda }=R{Z}^{2}\left(\dfrac{1}{{n}_{1}^{2}}-\dfrac{1}{{n}_{2}^{2}}\right)

∴λ∝1Z2∴\lambda \propto \dfrac{1}{{\text{Z}}^{2}}

λ1∝11{\lambda }_{1}\propto \dfrac{1}{1}

λ2∝11{\lambda }_{2}\propto \dfrac{1}{1}

λ3∝14{\lambda }_{3}\propto \dfrac{1}{4}

λ4∝19{\lambda }_{4}\propto \dfrac{1}{\text{9}}

∴λ1=λ2=4λ3=9λ4∴{\lambda }_{1}={\lambda }_{2}=4{\lambda }_{3}={9\lambda }_{4}

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