A gas containing hydrogen like ions with atomic no Z , emits photons in transition n +2 n , where n = Z . These photons fall on a metallic plate and eject electrons having minimum de-Broglie wavelength of 5 ~A ^ . Find the value of ' Z^ if

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A gas containing hydrogen like ions with atomic no Z , emits photons in transition n +2 n , where n = Z . These photons fall on a metallic plate and eject electrons having minimum de-Broglie wavelength of 5 ~A ^ . Find the value of ' Z^ if the work function of metal is 4.2 eV .

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Correct answer: 2

aligned E= & -(13.6 eV ) Z^2 ( 1 (Z+2)^2 - 1 Z^2 ) & =-13.6 ( Z^2-(Z+2)^2 (Z+2)^2 )= 4(Z+1) 13.6 (Z+2)^2 eV aligned ...(1) Now energy of electron is k= h^2 2 ^2 m ; (we have . = h 2 m k ) or, k=6 eV So, 4(Z+1) 13.6 (Z+2)^2 =6+4.2=10.2 eV Or, (Z+1) (Z+2)^2 = 3 16 (Z-2)(3 Z+2)=0 So, the value of Z=2 (neglecting the negative/fractional value)

A gas containing hydrogen like ions with atomic no Z , emits photons in transition n +2 n , where n = Z . These photons fall on a metallic plate and eject electrons having minimum de-Broglie wavelength of 5 ~A ^ . Find the value of ' Z^ if the work function of metal is 4.2 eV .

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