In coolidge tube the potential difference between cathode and anticathode is 120 kV. The maximum energy of emitted X-rays will be -

Options

A. `1.2 xx 10^(5)eV`
B. `10^(10)eV`
C. `10^(15)eV`
D. `10^(20)eV`

Answer

To find the maximum energy of emitted X-rays in a Coolidge tube with a potential difference of 120 kV, we can use the relationship between energy and potential difference. Here’s a step-by-step solution:

### Step 1: Understand the relationship between energy and potential difference
The energy (E) of the emitted X-rays is given by the equation:
\[ E = Q \cdot V \]
where:
- \( E \) is the energy in electron volts (eV),
- \( Q \) is the charge of the electron, and
- \( V \) is the potential difference in volts.

### Step 2: Identify the charge of the electron
The charge of an electron (\( Q \)) is approximately:
\[ Q = 1 \, e = 1.6 \times 10^{-19} \, \text{C} \]
However, in the context of X-ray energy, we can directly use the potential difference in kilovolts (kV) as it relates to electron volts.

### Step 3: Convert the potential difference from kilovolts to volts
Given that the potential difference (\( V \)) is 120 kV, we convert this to volts:
\[ V = 120 \, \text{kV} = 120 \times 10^3 \, \text{V} \]

### Step 4: Calculate the maximum energy of the emitted X-rays
Since 1 eV is defined as the energy gained by an electron when it is accelerated through a potential difference of 1 volt, we can directly use the potential difference in kV to find the energy in eV:
\[ E = V \]
Thus,
\[ E = 120 \, \text{kV} = 120 \times 10^3 \, \text{eV} \]

### Step 5: Express the energy in scientific notation
To express 120,000 eV in scientific notation:
\[ E = 1.2 \times 10^5 \, \text{eV} \]

### Final Answer
The maximum energy of the emitted X-rays will be:
\[ E = 1.2 \times 10^5 \, \text{eV} \]

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