If two pieces of caesium metal are supplied with energy `hv_(1) and hv_(2)` respectively and `v_(1) gt v_(2)` then which of the following relation does not hold true?

Options

A. `KE_(1) gt KE_(2)`
B. `(hv_(o))_(1) gt (hv_(o))_(2)`
C. `KE_(1) = hv_(1) - hv_(0)`
D. `KE_(2) = hv_(2) - hv_(o)`

Answer

To solve the problem, we need to analyze the relationships between the energies supplied to the cesium metal and how they relate to the work function and kinetic energy of the emitted electrons.

### Step-by-Step Solution:

1. **Understanding the Work Function**:
The work function (φ) is the minimum energy required to remove an electron from the surface of a metal. For cesium, this value is constant regardless of the energy supplied.

2. **Energy Supplied**:
We are given two energies supplied to the cesium metal: \( h\nu_1 \) and \( h\nu_2 \), where \( \nu_1 > \nu_2 \).

3. **Kinetic Energy Calculation**:
The kinetic energy (KE) of the emitted electrons can be calculated using the equation:
\[ KE = h\nu - \phi \]
Therefore, for the two energies, we have:
- For \( h\nu_1 \):
\[ KE_1 = h\nu_1 - \phi \]
- For \( h\nu_2 \):
\[ KE_2 = h\nu_2 - \phi \]

4. **Comparing Kinetic Energies**:
Since \( \nu_1 > \nu_2 \), it follows that:
\[ h\nu_1 > h\nu_2 \]
Subtracting the same work function φ from both sides gives:
\[ h\nu_1 - \phi > h\nu_2 - \phi \]
Thus, we can conclude:
\[ KE_1 > KE_2 \]

5. **Analyzing the Options**:
We need to determine which of the given relations does not hold true. The options typically involve comparisons of kinetic energies or energies supplied.

- **Option 1**: \( KE_1 > KE_2 \) (This is true)
- **Option 2**: \( h\nu_1 - \phi > h\nu_2 - \phi \) (This is also true)
- **Option 3**: \( KE_1 = h\nu_1 - \phi \) (This is true)
- **Option 4**: \( KE_2 = h\nu_2 - \phi \) (This is true)

6. **Identifying the Incorrect Relation**:
The incorrect relation is the one that contradicts our findings. Since we established that \( KE_1 > KE_2 \), any option suggesting otherwise would be incorrect.

### Conclusion:
The relation that does not hold true is the one that suggests \( KE_1 \) is not greater than \( KE_2 \).