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Characteristic X-rays of frequency 4.2 \times 10^{18} \mathrm{~Hz} are produced when transitions from L-shell K-shell take place in a certain target material. Use Mosley's law to determine the atomic number of the target material. Given Rydberg constant \mathrm{R=1.1 \times 10^7 \mathrm{~m}^{-1}}
 

Option: 1

\mathrm{Z=32}


 


Option: 2

\mathrm{Z=42}


Option: 3

\mathrm{Z=41}


Option: 4

\mathrm{Z=44}


Answers (1)

best_answer

\mathrm{\Delta E=h v=R h c(Z-b)^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) }

\mathrm{For \: \: K-series, b=1}

\mathrm{\therefore \quad v=R c(Z-1)^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) }

Substituting the values,

\mathrm{ 4.2 \times 10^{18}=\left(1.1 \times 10^7\right) 3 \times 10^8(Z-1)^2\left(\frac{1}{1}-\frac{1}{4}\right) }

\mathrm{ \therefore \quad(Z-1)^2=1697 }

\mathrm{ \text { or } \quad z-1 \approx 41 \text { or } Z=42 }




 

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manish

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