Atoms & Nuclei

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132 of 239

Question 132 of 239

If λ1{\lambda }_{1} and λ2{\lambda }_{2} are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ1:λ2{\lambda }_{1}:{\lambda }_{2} is :

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Answer: (A) 7:1357:135

1λ1=R[112−142]\dfrac{1}{{\lambda }_{1}}=R\left[\dfrac{1}{{1}^{2}}-\dfrac{1}{{4}^{2}}\right]
1λ2=R[132−142]\dfrac{1}{{\lambda }_{2}}=R\left[\dfrac{1}{{3}^{2}}-\dfrac{1}{{4}^{2}}\right]
λ1λ2=[19−116][1−116]=79×15\dfrac{{\lambda }_{1}}{{\lambda }_{2}}=\dfrac{\left[\dfrac{1}{9}-\dfrac{1}{16}\right]}{\left[1-\dfrac{1}{16}\right]}=\dfrac{7}{9\times 15}
λ1λ2=7135\dfrac{{\lambda }_{1}}{{\lambda }_{2}}=\dfrac{7}{135}

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