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 energy supplied to two pieces of cesium metal and how it relates to their kinetic energy and work function.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have two pieces of cesium metal supplied with energies \( hv_1 \) and \( hv_2 \) respectively, where \( v_1 > v_2 \). We need to determine which relation does not hold true based on the information given.

2. **Einstein's Photoelectric Equation**:
According to Einstein's photoelectric equation, the energy of the incoming photon is given by:
\[ E = \phi + KE \]
where \( E \) is the energy of the photon, \( \phi \) is the work function of the metal, and \( KE \) is the kinetic energy of the emitted electrons.

3. **Applying the Equation to Each Case**:
- For the first piece of cesium:
\[ hv_1 = \phi + KE_1 \]
Rearranging gives:
\[ KE_1 = hv_1 - \phi \]
- For the second piece of cesium:
\[ hv_2 = \phi + KE_2 \]
Rearranging gives:
\[ KE_2 = hv_2 - \phi \]

4. **Comparing Energies**:
Since \( v_1 > v_2 \), we have:
\[ hv_1 > hv_2 \]
This implies:
\[ KE_1 = hv_1 - \phi > KE_2 = hv_2 - \phi \]
Therefore, we can conclude that:
\[ KE_1 > KE_2 \]

5. **Work Function**:
The work function \( \phi \) is a property of the material and does not change between the two pieces of cesium. Thus:
\[ \phi_1 = \phi_2 = \phi \]

6. **Identifying the False Relation**:
Now, we can check the relations:
- \( KE_1 > KE_2 \) (True)
- \( KE_1 = hv_1 - \phi \) (True)
- \( \phi_1 > \phi_2 \) (False, as work functions are equal)

Thus, the relation that does not hold true is \( \phi_1 > \phi_2 \).

### Final Answer:
The relation that does not hold true is \( \phi_1 > \phi_2 \).