Which of the following are in the ascending order of wavelength?

Options

A. `H_(alpha), H_(beta),H_(gamma)`,…. Lines in the Balmer series of hydrogen atom
B. Lyman limit, Balmer limit, and Paschen limit in the hydrogen spectrum
C. Violet, blue, yellow, and red colour in solar spectrum.
D. None of above.

Explanation

To determine the ascending order of wavelength for the given series and colors, we can follow these steps:

### Step 1: Understand the Series
The question mentions the H-alpha, H-beta, and H-gamma lines of the Balmer series for the hydrogen atom. These transitions occur when electrons fall from higher energy levels to the second energy level (n=2).

### Step 2: Identify the Transitions
- **H-alpha (Hα)**: Transition from n=3 to n=2
- **H-beta (Hβ)**: Transition from n=4 to n=2
- **H-gamma (Hγ)**: Transition from n=5 to n=2

### Step 3: Energy and Wavelength Relationship
The energy difference (ΔE) between the energy levels is inversely proportional to the wavelength (λ) of the emitted light:
\[ \Delta E = \frac{hc}{\lambda} \]
Where:
- \( h \) = Planck's constant
- \( c \) = speed of light

This means that a larger energy difference corresponds to a shorter wavelength.

### Step 4: Determine Energy Differences
- The transition from n=3 to n=2 (Hα) has a smaller energy difference compared to the transition from n=4 to n=2 (Hβ) and n=5 to n=2 (Hγ).
- Therefore, the order of wavelengths from longest to shortest is:
- Hα (longest wavelength)
- Hβ (intermediate wavelength)
- Hγ (shortest wavelength)

### Step 5: Ascending Order of Wavelength
Thus, in ascending order of wavelength, we have:
\[ \lambda_{\text{Hγ}} < \lambda_{\text{Hβ}} < \lambda_{\text{Hα}} \]

### Step 6: Analyze Other Options
The question also mentions the Lyman limit, Balmer limit, and Paschen limit. The order of wavelengths for these series is:
- Lyman series (n=1) has the shortest wavelength.
- Balmer series (n=2) has a longer wavelength than Lyman.
- Paschen series (n=3) has the longest wavelength.

Thus, the ascending order for these series is:
\[ \lambda_{\text{Lyman}} < \lambda_{\text{Balmer}} < \lambda_{\text{Paschen}} \]

### Step 7: Color Wavelengths
For the colors mentioned (violet, blue, yellow, red), the order of wavelengths from shortest to longest is:
- Violet (shortest wavelength)
- Blue
- Yellow
- Red (longest wavelength)

### Final Answer
The ascending order of wavelengths for the given series and colors is:
1. Hγ
2. Hβ
3. Hα
4. Lyman
5. Balmer
6. Paschen
7. Violet
8. Blue
9. Yellow
10. Red