PrepRung
Sign inSign up free

JEE Main 2017 · Physics · Atoms, Nuclei and Dual Nature of Radiation · medium

The Kα X-ray line of copper (Z = 29) has wavelength 154 pm. Assuming Moseley's law, √(nu) propto (Z - 1), the wavelength of the Kα line of iron (Z =…

Single correct option

The KαK_\alpha X-ray line of copper (Z=29Z = 29) has wavelength 154 pm154\ \mathrm{pm}. Assuming Moseley's law, ν∝(Z−1)\sqrt{\nu} \propto (Z - 1), the wavelength of the KαK_\alpha line of iron (Z=26Z = 26) is nearly
  1. A. 193 pm193\ \mathrm{pm}
  2. B. 172 pm172\ \mathrm{pm}
  3. C. 138 pm138\ \mathrm{pm}
  4. D. 123 pm123\ \mathrm{pm}
Show answer and solution

Answer: (A) 193 pm193\ \mathrm{pm}

Moseley's law says ν=a2(Z−1)2\nu = a^2(Z-1)^2 for a given line, so λ=c/ν∝(Z−1)−2\lambda = c/\nu \propto (Z-1)^{-2}. Therefore λFeλCu=(29−126−1)2=(2825)2=1.2544\dfrac{\lambda_{\rm Fe}}{\lambda_{\rm Cu}} = \left(\dfrac{29-1}{26-1}\right)^2 = \left(\dfrac{28}{25}\right)^2 = 1.2544, giving λFe=154×1.2544≈193 pm\lambda_{\rm Fe} = 154\times1.2544 \approx 193\ \mathrm{pm}. The lighter element has the longer wavelength. Using λ∝1/(Z−1)\lambda\propto 1/(Z-1) gives 172 pm172\ \mathrm{pm}, and inverting the ratio gives 123 pm123\ \mathrm{pm}.
Report a mistake

Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake