Question

Identify the correct statements:
I. In the visible spectrum, violet light has highest frequency and red light has lowest frequency.
II. When white light is passed through a prism, violet light is deviated the most and red light is deviated the least.
III. Hydrogen atoms in gas phase exhibit line spectrum.

• A. I, II only
• B. I, III only
• C. II, III only
• D. I, II, III

Hint:

{VIBGYOR Trends:}

• $\lambda$: Increases from Violet to Red.
• Energy ($E=h\nu$) & Refractive Index ($\mu$): Increase from Red to Violet.
• Scattering ($\propto 1/\lambda^4$): Violet scatters most.

Answer 1

The Correct Option is D

Step 1: Analyze Statement I (Frequency Spectrum):
The relationship between frequency ($\nu$), wavelength ($\lambda$), and the speed of light ($c$) is given by $c = \nu \lambda$. Since $c$ is constant, frequency is inversely proportional to wavelength ($\nu \propto 1/\lambda$). In the visible spectrum:

• Red Light: Has the longest wavelength ($\approx 700$ nm), corresponding to the lowest frequency.
• Violet Light: Has the shortest wavelength ($\approx 400$ nm), corresponding to the highest frequency.

Thus, Statement I is correct.
Step 2: Analyze Statement II (Dispersion through Prism):
According to Cauchy's dispersion formula, the refractive index ($\mu$) of a material is inversely related to the square of the wavelength ($\mu = A + B/\lambda^2$).

• Since $\lambda_{violet}<\lambda_{red}$, the refractive index is higher for violet ($\mu_{violet}>\mu_{red}$).
• The angle of deviation ($\delta$) produced by a thin prism is given by $\delta = (\mu - 1)A$.
• Consequently, $\delta_{violet}>\delta_{red}$. Violet deviates the most, and red deviates the least.

Thus, Statement II is correct.
Step 3: Analyze Statement III (Hydrogen Spectrum):
When hydrogen gas is excited (e.g., by electric discharge), the electrons absorb energy and jump to higher energy levels. When they return to lower energy levels, they emit electromagnetic radiation at specific, discrete frequencies. This results in a discontinuous spectrum consisting of sharp lines (Lyman, Balmer, Paschen, etc.), known as a Line Spectrum. Continuous spectra are characteristic of hot dense bodies (like stars/bulbs), not atomic gases. Thus, Statement III is correct.
Step 4: Conclusion:
All three statements are physically and chemically correct.