The charge of an electron is `1.6 × 10^(-19) C` . How many electrons strike the screen of a cathode ray tube each second when the beam current is 16 mA

Options

A. `10^(17)`
B. `10^(19)`
C. `10^(-19)`
D. `10^(-17)`

Answer

To find the number of electrons striking the screen of a cathode ray tube each second when the beam current is 16 mA, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Current, Charge, and Time**:
The current (I) is defined as the amount of charge (Q) flowing per unit time (t). Mathematically, this is expressed as:
\[ I = \frac{Q}{t} \]
Rearranging this gives us:
\[ Q = I \times t \]

2. **Convert the Current to Standard Units**:
The given current is 16 mA (milliamperes). We need to convert this to amperes:
\[ 16 \, \text{mA} = 16 \times 10^{-3} \, \text{A} \]

3. **Calculate the Charge Flowing in One Second**:
We want to find the charge flowing in 1 second (t = 1 s):
\[ Q = I \times t = (16 \times 10^{-3} \, \text{A}) \times (1 \, \text{s}) = 16 \times 10^{-3} \, \text{C} \]

4. **Determine the Charge of One Electron**:
The charge of a single electron (e) is given as:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

5. **Calculate the Number of Electrons**:
If n is the number of electrons striking the screen, then the total charge Q can also be expressed as:
\[ Q = n \times e \]
Substituting the values we have:
\[ 16 \times 10^{-3} = n \times (1.6 \times 10^{-19}) \]
Rearranging to solve for n gives:
\[ n = \frac{16 \times 10^{-3}}{1.6 \times 10^{-19}} \]

6. **Perform the Calculation**:
\[ n = \frac{16}{1.6} \times \frac{10^{-3}}{10^{-19}} = 10 \times 10^{16} = 10^{17} \]

### Final Answer:
The number of electrons striking the screen of the cathode ray tube each second is:
\[ n = 10^{17} \]