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An element of atomic number 9 emits K(al...

An element of atomic number 9 emits `K_(alpha)` X-ray of wavelength `lamda`. Find the atomic number of the element which emits `K_(alpha)` X-ray of wavelength `4lamda`.

A

11

B

44

C

6

D

5

Text Solution

Verified by Experts

The correct Answer is:
C
According to Moseley.s equation,
Squaring both side, `sqrt(upsilon)=a(Z-b)`
`" "upsilon=a^(2)(Z-b)^(2)" or, "c/lambda=a^(2)(Z-b)^(2)`
Therefore, for two different elements the ratio of wavelengths is given by
`lambda_(1)/lambda_(2)=(Z_(2)-1)^(2)/(Z_(1)-1)^(2)`
`lambda_(1)=lambda, Z_(1)=11, lambda_(2)=4lambda, Z_(2)=?`
`therefore lambda/(4lambda)=(Z_(2)-1)^(2)/(11-1)^(2) rArr (Z_(2)-1)^(2)=25 rArr Z_(2)=6`.
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