X-ray from a tube with a target A of atomic number Z shows strong K- lines for target A and two weak K- lines for impurities- The wavelength of K- lines is -0 for target A and -1 and -2 for two impurities respectively- -0-1- 4 and -0-2-14- The screening constant of K- lines is unity- Select the correct alternatives -

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Byju's Answer

Standard XII

Physics

Moseley's Law

X-ray from a ...

Question

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) :

The atomic number of first impurity is

2 Z - 1

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The atomic number of first impurity is

2 Z + 1

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The atomic number of second impurity is

\frac{Z + 1}{2}

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The atomic number of second impurity is

\frac{Z}{2} + 1

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Solution

The correct options are
A The atomic number of first impurity is $2 Z - 1$
B The atomic number of second impurity is $\frac{Z + 1}{2}$
$\frac{λ_{0}}{λ_{1}} = 4 \Rightarrow \frac{(Z_{1} - 1)^{2}}{(Z - 1)^{2}} = 4 \Rightarrow Z_{1} = 2 Z - 1$

$\frac{λ_{0}}{λ_{2}} = \frac{1}{4} \Rightarrow \frac{(Z_{2} - 1)^{2}}{(Z - 1)^{2}} = \frac{1}{4} \Rightarrow Z_{2} = \frac{Z + 1}{2}$

So, the answers are option (A) & (C).

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Similar questions

X -

ray from a tube with a target

A

of atomic number

Z

shows strong

K -

lines for target

A

and weak

K -

lines for impurities. The wavelength of

K_{α}

lines is

λ_{α}

for target

A

and

λ_{1}

and

λ_{2}

for two impurities.

\frac{λ_{α}}{λ_{1}} = 4 and \frac{λ_{α}}{λ_{2}} = \frac{1}{4}

Assuming the screening constant of

K_{α}

lines to be unity. The atomic number of the impurities

Z_{1}

and

Z_{2}

Q. X-ray from a tube with a target

A

of atomic number

Z

shows strong

K

lines for target

A

and weak

K

lines for impurities. The wavelength of

K_{α}

lines is

λ_{z}

for target

A

and

λ_{1}

and

λ_{2}

for two impurities.

\frac{λ_{z}}{λ_{1}} = 4 a n d \frac{λ_{z}}{λ_{2}} = \frac{1}{4}

Assuming the screening constant of

K_{α}

lines to be unity, select the correct statement(s)

X -

ray from a tube with a target

A

of atomic number

Z

shows strong

K -

lines for target

A

and weak

K -

lines for impurites. The wavelength of

K_{α}

lines is

λ_{z}

for target

A

and

λ_{1}

and

λ_{2}

for two impurities.

\frac{λ_{z}}{λ_{1}} = 4 and \frac{λ_{z}}{λ_{2}} = \frac{1}{4}

Assuming the screening constant of

K_{α}

lines to be unity, select the correct statement(s).

Q. Target of a coolidge tube contains two impurities. Atomic number of the target is Z and that of

1^{s t}

and

2^{n d}

impurities is

Z_{1} and Z_{2} .

Wavelength of

K_{α}

lines of target is

λ

and that of impurities are

λ_{1}

and

λ_{2}

where,

\frac{λ}{λ_{1}} = 4

and

\frac{λ}{λ_{2}} = \frac{1}{4}

, then

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

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The correct options are A The atomic number of first impurity is 2Z−1 B The atomic number of second impurity is Z+12λ0λ1=4⇒(Z1−1)2(Z−1)2=4⇒Z1=2Z−1λ0λ2=14⇒(Z2−1)2(Z−1)2=14⇒Z2=Z+12So, the answers are option (A) & (C).