Question

According to Einstein’s photoelectric equation to the graph between kinetic energy of photoelectrons ejected and the frequency of incident radiation is

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is D

The Fundamental Equation

Einstein's photoelectric equation establishes the relationship:

\[ K_{\text{max}} = h\nu - \phi \]

where:

• \( K_{\text{max}} \) = Maximum kinetic energy of ejected electrons
• \( h \) = Planck's constant (\( 6.626 \times 10^{-34} \) Js)
• \( \nu \) = Frequency of incident light
• \( \phi \) = Work function (material-specific energy threshold)

The equation can be viewed as a linear function:

\[ y = mx + c \]

where:

• \( y = K_{\text{max}} \) (Dependent variable)
• \( x = \nu \) (Independent variable)
• \( m = h \) (Slope)
• \( c = -\phi \) (Y-intercept)

Slope (h)

The positive slope indicates:

• Direct proportionality between kinetic energy and frequency
• Higher frequency light results in more energetic photoelectrons
• The slope's value equals Planck's constant

Y-intercept (-φ)

The negative intercept reveals:

• No electron emission occurs below the threshold frequency
• The magnitude represents the work function
• X-intercept (\( \nu_0 = \phi/h \)) marks the minimum frequency for emission

The correct answer is (D) :