Charateristic X-rays are not obtained in the spectrum of H-atom bacause-

Options

A. hydrogen is a gas
B. hydrogen is very light
C. energy difference in enerfy levels fo hydrogen is much less
D. energy difference in enerfy levels of hydrogen is not true

Explanation

### Step-by-Step Solution:

1. **Understanding Characteristic X-rays**: Characteristic X-rays are produced when an electron transitions between energy levels in an atom, resulting in the emission of X-ray photons. This process typically occurs in heavier elements where the energy differences between electron shells are significant.

2. **Energy Levels in Hydrogen Atom**: The energy levels of the hydrogen atom can be calculated using the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number (n=1, 2, 3,...). For hydrogen (Z=1), the energy levels are:
- For \( n=1 \): \( E_1 = -13.6 \, \text{eV} \)
- For \( n=2 \): \( E_2 = -3.4 \, \text{eV} \)
- For \( n=3 \): \( E_3 = -1.51 \, \text{eV} \)

3. **Energy Differences**: The energy differences between these levels are relatively small. For example:
- The transition from \( n=1 \) to \( n=2 \) gives:
\[ \Delta E = E_2 - E_1 = -3.4 \, \text{eV} - (-13.6 \, \text{eV}) = 10.2 \, \text{eV} \]
- The transition from \( n=2 \) to \( n=3 \) gives:
\[ \Delta E = E_3 - E_2 = -1.51 \, \text{eV} - (-3.4 \, \text{eV}) = 1.89 \, \text{eV} \]

4. **Comparison with X-ray Energy**: Characteristic X-rays typically have energies in the range of 100 keV (100,000 eV) to a few hundred keV. The energy differences in the hydrogen atom are orders of magnitude lower than this range.

5. **Conclusion**: Since the energy differences in the hydrogen atom are too small to produce characteristic X-rays, characteristic X-rays are not obtained in the spectrum of the hydrogen atom.

### Final Answer:
Characteristic X-rays are not obtained in the spectrum of the hydrogen atom because the energy differences between the electron energy levels in hydrogen are too small compared to the high energy required for characteristic X-ray emission.

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