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) :

 

Answer 2

Step 1: Recall Photoelectric Equation

Einstein's photoelectric equation: $KE_{max} = hf - \phi_0$

Step 2: Identify Graph Type

Equation is in form $y = mx + c$, representing a straight line.

y-axis: $KE_{max}$

x-axis: frequency ($f$)

slope ($m$): $h$ (Planck's constant, positive)

y-intercept ($c$): $-\phi_0$ (negative, as work function $\phi_0$ is positive)

Step 3: Analyze Graph Properties

- Straight line with positive slope.
- y-intercept is negative (extending line to y-axis).
- Threshold frequency ($f_0$) exists (x-intercept where $KE = 0$).

Step 4: Evaluate Option (A)

- Negative slope: Correct.

Step 5: Evaluate Option (B)

- Positive slope, starts at origin: Work function is zero (special case, less general).

Step 6: Evaluate Option (C)

- Positive slope, negative y-intercept, threshold frequency: Incorrect.

Step 7: Evaluate Option (D)

- Non-linear at start: Correct for linear equation.

Step 8: Select Best Match

Option (D) best represents the photoelectric equation.

Final Answer: The final answer is ${(D)}$