Which of the following is wrong?

Options

A. Cathode rays have constant e/m ratio.
B. e/m ratio of anode rays is not constant.
C. e/m ratio of protons is not constant
D. e/m ratio of `beta`-particles is constant.

Answer

To determine which of the statements is wrong, we need to analyze the given options regarding the E/m (charge-to-mass ratio) for cathode rays, anode rays, protons, and beta particles.

### Step-by-Step Solution:

1. **Understanding Cathode Rays**:
- Cathode rays are streams of electrons, which are negatively charged particles.
- The charge (e) of an electron is approximately \(1.6 \times 10^{-19}\) coulombs.
- The mass (m) of an electron is approximately \(9.1 \times 10^{-31}\) kg.
- The E/m ratio for electrons can be calculated as:
\[ \frac{E}{m} = \frac{1.6 \times 10^{-19}}{9.1 \times 10^{-31}} \approx 1.75 \times 10^{11} \, \text{C/kg} \]
- This ratio is constant for cathode rays.

2. **Understanding Anode Rays**:
- Anode rays consist of positively charged particles (like protons, alpha particles, etc.).
- The E/m ratio for anode rays is not constant because it depends on the type of positive ion present (e.g., protons, alpha particles, etc.), as they have different charges and masses.

3. **E/m Ratio for Protons**:
- The charge of a proton is also \(1.6 \times 10^{-19}\) coulombs.
- The mass of a proton is approximately \(1.67 \times 10^{-27}\) kg.
- The E/m ratio for protons can be calculated as:
\[ \frac{E}{m} = \frac{1.6 \times 10^{-19}}{1.67 \times 10^{-27}} \approx 9.58 \times 10^{7} \, \text{C/kg} \]
- This ratio is constant for protons.

4. **E/m Ratio for Beta Particles**:
- Beta particles can be electrons (negatively charged) or positrons (positively charged).
- The charge and mass of beta particles are constant, so the E/m ratio for beta particles is also constant.

5. **Identifying the Wrong Statement**:
- The statement that "E/m ratio for protons is not constant" is incorrect because the E/m ratio for protons is indeed constant.
- Therefore, this statement is the wrong one.

### Conclusion:
The wrong statement is that "E/m ratio for protons is not constant."

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