X-rays emitted from a copper target and a molybdenum target are found to contain a line of wavelength 22-85 nm attributed to the K- line of an impurity element- The K- lines of copper Z - 29 and molybdenum Z - 42 have wavelengths 15-42 nm and 7-12 nm- respectively- The atomic number of the impurity element is

The correct option is C 24 For K_α line, 1/λ=3R(Z 1)^2/4 So, λ_copper/λ_impurity=(Z_impurity 1)^2(Z_copper 1)^2 ⇒ 15.42/22.85=(Z_imp ...

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Byju's Answer

Standard XII

Physics

The Photon Model

X-rays emitte...

Question

$X -$ rays emitted from a copper target and a molybdenum target are found to contain a line of wavelength $22.85 n m$ attributed to the $K_{α}$ line of an impurity element. The $K_{α}$ lines of copper $(Z = 29)$ and molybdenum $(Z = 42)$ have wavelengths $15.42 n m$ and $7.12 n m$ , respectively. The atomic number of the impurity element is

22

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Solution

The correct option is C $24$
For $K_{α}$ line, $1 / λ = 3 R (Z - 1)^{2} / 4$

So, $λ_{c o p p e r} / λ_{i m p u r i t y} = \frac{(Z_{i m p u r i t y} - 1)^{2}}{(Z_{c o p p e r} - 1)^{2}}$ $\Rightarrow 15.42 / 22.85 = \frac{(Z_{i m p u r i t y} - 1)^{2}}{28^{2}}$ $\Rightarrow (Z_{i m p u r i t y} - 1)^{2} = 529$ $

$\Rightarrow Z_{i m p u r i t y} = 24$

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Similar questions

Q. X - rays emitted from a copper target and a molybdenum target are found to contain a line of wavelength 22.85 nm attributed to the Ka line of an impurity element. The Ka lines of copper (Z = 29) and molybdenum (Z = 42) have wavelength 15.42 nm and 15.42 nm and 7.12 nm respectively. Using Moseley's law

γ^{\frac{1}{2}} = a (Z - b)

. Calculate the atomic number of the impurity element.

Q. X-rays emitted from a copper target and a molybdenum target are found to contain a line of wavelength

22.85

nm attribute to the

K_{α}

lines of an impure element. The

K_{α}

lines of copper (Z

= 29

) and molybdenum (Z

= 42

) have a wavelength

15.42

nm and

7.12

nm respectively. Using Moseley's law,

v^{1 / 2} = a (Z - b)

, calculate the atomic number of the impure element:

Q. An

X -

ray tube with a copper target is found to emit lines other those due to copper. The

K_{α}

line of copper is known to have a wavelength

1.5405 A

and the other two

K_{α}

lines observed have wavelength

0.7092 A

and

1.6578 A

. Identify the impurities (find the value of

Z

, atomic number).

Q. If

λ_{c u}

is the wavelength of

K_{α},

X-ray line of copper (atomic number 29) and

λ_{M o}

is the wavelength of the

K_{α}

X-ray line of molybdenum (atomic number 42), then the ratio

λ_{c u} / λ_{M o}

is close to :

Q. X-ray from a tube with a target A of atomic number Z shows strong

K_{α}

lines for target A and two weak

K_{α}

lines for impurities. The wavelength of

K_{α}

lines is

λ_{0}

for target A and

λ_{1}

and

λ_{2}

for two impurities respectively.

\frac{λ_{0}}{λ_{1}} = 4

and

\frac{λ_{0}}{λ_{2}} = \frac{1}{4}

. The screening constant of

K_{α}

lines is unity. Select the correct alternative(s) :

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The correct option is C 24For Kα line, 1/λ=3R(Z−1)2/4So, λcopper/λimpurity=(Zimpurity−1)2(Zcopper−1)2 ⇒15.42/22.85=(Zimpurity−1)2282 ⇒(Zimpurity−1)2=529 $⇒Zimpurity=24