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- lines is -z for target A and -1 and -2 for two impurities- -z-1-4 and -z-2-14Assuming the screening constant of K- lines to be unity- select the correct statements-

According to moseley's law: λ∝1(z 1)^2 ; λ_zλ_1=(z_1 1)^2(z 1)^2 From the data given in the question, z_1 1z 1=2⇒ z_1=2z 1 Similarly, λ_zλ_2=z_2 1)^2(z 1)^ ...

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Byju's Answer

Standard XII

Physics

Doppler Effect in Light Waves

X- ray from a...

Question

$X -$ 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).

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 option is C The atomic number of second impurity is $\frac{z + 1}{2}$ .
According to moseley's law: $λ \propto \frac{1}{(z - 1)^{2}}; \frac{λ_{z}}{λ_{1}} = \frac{(z_{1} - 1)^{2}}{(z - 1)^{2}}$

From the data given in the question,

$\frac{z_{1} - 1}{z - 1} = 2 \Rightarrow z_{1} = 2 z - 1$

Similarly, $\frac{λ_{z}}{λ_{2}} = \frac{z_{2} - 1)^{2}}{(z - 1)^{2}}$

From the data given in the question,

$\frac{z_{2} - 1}{z - 1} = \frac{1}{2} \Rightarrow z_{2} = \frac{z + 1}{2}$

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Similar questions

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 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_{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) :

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

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).

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The correct option is C The atomic number of second impurity is z+12.According to moseley's law: λ∝1(z−1)2 ; λzλ1=(z1−1)2(z−1)2 From the data given in the question, z1−1z−1=2⇒z1=2z−1 Similarly, λzλ2=z2−1)2(z−1)2 From the data given in the question, z2−1z−1=12⇒z2=z+12