Concepts Of Physics MCQ Edition [Volume 2]PhysicsX-rays
In a photoelectric experiment, the stopping potential exhibits a linear relationship with the inverse of the wavelength (1/ ) of the light incident on the cathode. Additionally, the potential difference applied across an X-ray tube is linearly related to the inverse of the cutoff wavelength (1/ ) of the emitted X-rays. Determine the value of the common slope of the lines in these two scenarios.
Options
- A1.242 10⁻⁶ V m
- B1.242 10⁻⁹ V m
- C1.242 10⁻⁵ V m
- D1.242 10⁻⁷ V m
Correct answer
A. 1.242 10⁻⁶ V m
Step-by-step solution
From Einstein's photoelectric equation, the stopping potential V₀ is given by: eV₀ = hc - V₀ = hc e ( 1 ) - e The slope of the graph of V₀ versus 1/ is hc e . For an X-ray tube, the cutoff wavelength _c is given by: eV = hc _c V = hc e ( 1 _c ) The slope of the graph of V versus 1/ _c is also hc e . The common slope is hc e . Substituting the standard values h = 6.626 10⁻³⁴ J s , c = 3 10^8 m/s , and e = 1.6 10⁻¹⁹ C : Slope = 6.626 10⁻³⁴ 3 10^8 1.6 10⁻¹⁹ Slope = 12.42 10⁻⁷ V m = 1.242 10⁻⁶ V m