Calculate the wavelength of the k_a line for z=31 , when a=5 × 10^7 ~Hz^ 1 / 2 for a characteristic X-ray spectrum.

Correct answer: A. 1.33 Å Given, z=31 and a=5 × 10^7 ~Hz^ 1 / 2 aligned v & =a(z-1) or v & =a^2(z-1)^2 & =(5 × 10^7)^2(31-1)^2 & =25 × 10^ 14 × 30 × 30 & =2.25 × 10^ 18 ~Hz & =(c)/(λ) λ=(c)/(v) & = 3 × 10^8 ~ms^ -1 2.25 × 10^ 18 ~Hz & =1.33 × 10^ -10 ~m & =1.33 Å aligned

JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Electromagnetic Waves

JEE Main · Physics · Electromagnetic Waves

Calculate the wavelength of the k_a line for z=31 , when a=5 × 10^7...

Calculate the wavelength of the

k_a

line for

z=31

, when

a=5 \times 10^7 \mathrm{~Hz}^{1 / 2}

for a characteristic X-ray spectrum.

Options

A $1.33 Å$
B $1.33 \mathrm{~nm}$
C $133 \times 10^{-10} \mathrm{~m}$
D $133 \mathrm{~nm}$

Correct answer

A. $1.33 Å$

Step-by-step solution

Given,

z=31

and

a=5 \times 10^7 \mathrm{~Hz}^{1 / 2}

\begin{aligned} \sqrt{v} & =a(z-1) \\ \text { or } \quad v & =a^2(z-1)^2 \\ & =\left(5 \times 10^7\right)^2(31-1)^2 \\ & =25 \times 10^{14} \times 30 \times 30 \\ & =2.25 \times 10^{18} \mathrm{~Hz} \\ \therefore \quad & =\frac{c}{\lambda} \Rightarrow \lambda=\frac{c}{v} \\ & =\frac{3 \times 10^8 \mathrm{~ms}^{-1}}{2.25 \times 10^{18} \mathrm{~Hz}} \\ & =1.33 \times 10^{-10} \mathrm{~m} \\ & =1.33 Å \end{aligned}

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