This question involves the photoelectric effect, which describes how electrons are emitted from a material when light shines on it. Let's analyze both statements step by step.

Step 1: Understanding the Photoelectric Effect Equations

The key equation for the photoelectric effect is Einstein's photoelectric equation:

$K\max =h\nu -\varphi$

where:

• $K\max$ is the maximum kinetic energy of the emitted photoelectrons,
• $h$ is Planck's constant,
• $\nu$ is the frequency of the incident light,
• $\varphi$ is the work function of the material (the minimum energy needed to eject an electron, $\varphi =h{\nu }_0$).

The stopping potential $V_0$ is the minimum voltage needed to stop the most energetic photoelectrons. It is related to $K\max$ by:

$K\max =e{V}_0$

where $e$ is the charge of an electron. Combining these, we get:

$e{V}_0=h\nu -\varphi$

or

$V_0=\frac{h\nu -\varphi }{e}$

Step 2: Analyzing Statement-1

Statement-1 claims: If the frequency is doubled (from $\nu$ to $2\nu$), both $K\max$ and $V_0$ are doubled.

Let's test this with the equations. Initially:

$K_{max1}=h\nu -\varphi$

After doubling the frequency:

$K_{max2}=h\left(2\nu \right)-\varphi =2h\nu -\varphi$

Is $K_{max2}=2K_{max1}$? Let's check:

$2K_{max1}=2(h\nu -\varphi )=2h\nu -2\varphi$

But $K_{max2}=2h\nu -\varphi$. These are equal only if $\varphi =0$, which is not true for any real material. Therefore, $K\max$ is not doubled when frequency is doubled. The same logic applies to stopping potential $V_0$ since it is directly proportional to $K\max$. Thus, Statement-1 is false.

Step 3: Analyzing Statement-2

Statement-2 claims: $K\max$ and $V_0$ are linearly dependent on the frequency of incident light.

From the equations:

$K\max =h\nu -\varphi$

$V_0=\frac{h}{e}\nu -\frac{\varphi }{e}$

Both equations are of the form $y=mx+c$, where $y$ is $K\max$ or $V_0$, $x$ is $\nu$, $m$ is a constant ($h$ or $\frac{h}{e}$), and $c$ is a constant ($-\varphi$ or $-\frac{\varphi }{e}$). This is the definition of a linear relationship. Therefore, Statement-2 is true.

Step 4: Final Answer

Since Statement-1 is false and Statement-2 is true, the correct choice is:

Statement-1 is false, Statement-2 is true.

Related Topics and Formulae

Key Formulae:

• Einstein's Photoelectric Equation: $K\max =h\nu -\varphi$
• Stopping Potential: $K\max =e{V}_0$ or $V_0=\frac{h\nu -\varphi }{e}$
• Work Function: $\varphi =h{\nu }_0$

Related Topics: The photoelectric effect is a fundamental phenomenon in quantum physics that demonstrates the particle nature of light (photons). It is crucial for understanding concepts like quantization of energy, wave-particle duality, and the interaction of light with matter.