If the series limit of the Balmer series for hydrogen is 2700 A ˚ . Calculate the atomic no. of the element which gives X-ray wavelength of K α line as 1.0 A ˚ .

Balmer limit: 2700 1 = R ( 2 2 1 − ∞ 2 1 ) = 4 R K α : 1 1 = R ( Z − 1 ) 2 ( 1 2 1 − 2 2 1 ) = R ( Z − 1 ) 2 ⋅ 4 3 Dividing: 2700 = ( Z − 1 ) 2 × 3 ⇒ ( Z − 1 ) 2 = 900 Z = 31.

Start Free Mock LoginAlready registered? Login here

Physics - Modern Physics Question with Solution | TestHub

PhysicsModern PhysicsX-raysMedium2 minQB

PhysicsMediumsingle choice

If the series limit of the Balmer series for hydrogen is $2700 \overset{˚}{A}$ . Calculate the atomic no. of the element which gives X-ray wavelength of $K_{α}$ line as $1.0 \overset{˚}{A}$ .

Options:

Answer:

Solution:

Balmer limit: $\frac{1}{2700} = R (\frac{1}{2 ^{2}} - \frac{1}{\infty ^{2}}) = \frac{R}{4}$

$K_{α} : \frac{1}{1} = R (Z - 1)^{2} (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}) = R (Z - 1)^{2} \cdot \frac{3}{4}$

Dividing: $2700 = (Z - 1)^{2} \times 3 \Rightarrow (Z - 1)^{2} = 900$

$Z = 31.$

Subject:PhysicsTopic:Modern PhysicsSubtopic:X-rays

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...