Identify the graph behavior for a black body

For black body radiation:

• As temperature increases, the total intensity increases.
• The peak shifts to shorter wavelength.

So the curve with the peak farthest to the left and highest intensity corresponds to the highest temperature.

Check statement A

From the spectrum, the leftmost/highest peak corresponds to $T_4$, then $T_3$, then $T_2$, then $T_1$. Hence, $T_4 > T_3 > T_2 > T_1$ So A is correct.

Check statement B

The classical model that tried to explain black body radiation assumed oscillators behaving like simple harmonic oscillators in the cavity walls. But the statement says:

"The black body consists of particles performing simple harmonic motion."

This is not a correct statement about the black body itself. A black body is an ideal absorber/emitter; the radiation explanation involves oscillators in cavity walls, not that the black body "consists of particles performing SHM" as a defining statement.

So B is incorrect.

Check statement C

By Wien's displacement law, $\lambda_{\max} T = \text{constant}$ Therefore, when $T$ increases, $\lambda_{\max}$ decreases.

So the peak shifts to shorter wavelength as temperature increases. Hence C is correct.

Check statement D

The statement is $\frac{T_1}{\nu_1} = \frac{T_2}{\nu_2} = \frac{T_3}{\nu_3} = \text{constant}$

Using Wien's law in frequency form, $\nu_{\max} \propto T$ Hence, $\frac{T}{\nu_{\max}} = \text{constant}$

So this relation is correct in principle for the peak frequencies. Therefore D is correct if $\nu_1,\nu_2,\nu_3$ denote the corresponding peak frequencies.

However, in standard black body spectrum graphs shown against wavelength, the marked quantities are often wavelengths, not frequencies. Since the statement explicitly uses $\nu$, it refers to frequency maxima, and Wien's frequency version indeed gives $T/\nu_{\max}=\text{constant}$.

Thus D is correct.

Check statement E

Black body radiation was successfully explained by Planck's quantum theory, i.e. by quantisation of energy.

So E is correct.

Count correct statements

Correct statements: A, C, D, E

Number of correct statements $= 4$.

Compare with stored answer

Stored correct answer is 2, but the derived answer is 4.

The likely reason for discrepancy is statement D may have been interpreted from a wavelength-spectrum graph while using frequency incorrectly, and statement B might be considered true in a loose textbook sense only for cavity oscillators. Still, as written, the scientifically consistent evaluation gives 4.