Question

If the operating potential in an X-ray tube is increased by 1%, by what percentage does the cutoff wavelength decrease?

Answer 1

Dear Student,

◆ Answer -

∆λ/λ % = 1 %

● Explanation -

Cutoff wavelength of X-ray radiation is given by -

λ = hc/V

New wavelength is -

λ' = hc/1.01V

λ' = λ/1.01

Change in wavelength is given by -

∆λ = λ-λ'

∆λ = λ - λ/1.01

∆λ = 0.01λ/1.01

So, percent change in wavelength is given by -

∆λ/λ % = (0.01λ/1.01) × 100 / λ

∆λ/λ % = 1/1.01

∆λ/λ % = 0.9901

∆λ/λ % ~ 1 %

Change in % wavelength is 1 %.

Thanks dear. Hope this helps you..

Answer 2

The percentage of the cutoff wavelength decrease is approximately 1

Explanation:

• Let us consider that V is the operating potential and λ is the cut-off wavelength in the X-ray tube.

Then,

• Λ = hcV

where,

• h = Constant of Planck  
• c = Light’s speed

• When there is an increase in the operating voltage by 1%, then the voltage of new operation (V‘) will be shown as V’ = V + VV’ x 1100 = 1.01 V.

• On increasing the operating voltage, the cut off wavelength λ’ is shown as λ’ = λ1.01.

• Therefore, λ’ – λ = 0.011.01λ

• The wavelength’s percentage change is shown as  

• 0.01λ1.01 × λ × 100 = 0.9901 = approximately 1.