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 -

The correct options are B The atomic number of second impurity is Z+12 C The atomic number of first impurity is 2Z 1 λ_0λ_1=4 #160; #160 ...

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

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

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 -

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K_{α}

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λ_{α}

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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}

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Z_{1}

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Z_{2}

Q. X-ray from a tube with a target

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of atomic number

Z

shows strong

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A

and weak

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lines for impurities. The wavelength of

K_{α}

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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}

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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}

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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}

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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

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\frac{λ}{λ_{2}} = \frac{1}{4}

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K_{α}

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and molybdenum

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15.42 n m

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The correct options are B The atomic number of second impurity is Z+12 C The atomic number of first impurity is 2Z−1λ0λ1=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).