The e/m ratio for cathode rays

Options

A. is a constant value regardless of the nature of gas taken in the tube
B. varies as the atomic number of the element forming cathode in the discharge tube changes
C. varies as atomic number of the gas in the tube varies
D. has the smallest value when the discharge tube is filled with hydrogen

Answer

To find the e/m (charge-to-mass) ratio for cathode rays, we can follow these steps:

### Step 1: Understand the Components of e/m Ratio
The e/m ratio represents the specific charge of a particle, where:
- **e** is the charge of the particle (in this case, the electron).
- **m** is the mass of the particle (also the mass of the electron).

### Step 2: Identify the Charge of the Electron
The charge of the electron is a known constant:
- \( e = 1.6 \times 10^{-19} \) coulombs.

### Step 3: Identify the Mass of the Electron
The mass of the electron is also a known constant:
- \( m = 9.1 \times 10^{-31} \) kg.

### Step 4: Calculate the e/m Ratio
To find the e/m ratio, we divide the charge of the electron by its mass:
\[ \frac{e}{m} = \frac{1.6 \times 10^{-19} \text{ C}}{9.1 \times 10^{-31} \text{ kg}} \]

### Step 5: Perform the Calculation
Calculating the above expression:
\[ \frac{e}{m} \approx 1.758 \times 10^{11} \text{ C/kg} \]

### Step 6: Conclusion
The e/m ratio for cathode rays, which are composed of electrons, is approximately \( 1.758 \times 10^{11} \text{ C/kg} \). This value is a constant and does not depend on the nature of the gas in the discharge tube.

### Summary
- The e/m ratio for cathode rays is a constant value of approximately \( 1.758 \times 10^{11} \text{ C/kg} \).
- This ratio is independent of the medium through which the cathode rays travel.

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