Atoms & Nuclei

JEE Main level, single correct, medium

129 of 239

Question 129 of 239

A particular hydrogen like ion emits radiation of frequency 2.92×1015Hz2.92\times {10}^{15}Hz when it makes transition from n=3n=3 to n=1n=1. The frequency in HzHz of radiation emitted in transition from n=2n=2 to n=1n=1 will be:

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Answer: (B) 2.46×10152.46\times {10}^{15}

As we know,
ν∝[1n12−1n22]\nu \propto \left[\dfrac{1}{{n}_{1}^{2}}-\dfrac{1}{{n}_{2}^{2}}\right]
2.92×1015ν=[11−19][11−14]\dfrac{2.92\times {10}^{15}}{\nu }=\dfrac{\left[\dfrac{1}{1}-\dfrac{1}{9}\right]}{\left[\dfrac{1}{1}-\dfrac{1}{4}\right]}
ν=2.92×1015×34×98\nu =2.92\times {10}^{15}\times \dfrac{3}{4}\times \dfrac{9}{8}
ν=2.46×1015Hz\nu =2.46\times {10}^{15}Hz

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