Radiation from hydrogen discharge tube falls on a cesium plate find the maximum possible kinetic energy of the photeelectron work function of cesium is `1.9ev`

Explanation

To find the maximum possible kinetic energy of the photoelectron when radiation from a hydrogen discharge tube falls on a cesium plate, we can use the Einstein photoelectric equation:

\[ K.E. = E - \phi \]

where:
- \( K.E. \) is the kinetic energy of the emitted photoelectron,
- \( E \) is the energy of the incident photon,
- \( \phi \) is the work function of the material (in this case, cesium).

### Step 1: Determine the energy of the incident photon
The energy of the photon emitted from the hydrogen discharge tube can be calculated using the formula for the energy levels of hydrogen:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

For the transition from \( n = 2 \) to \( n = 1 \) (which gives the maximum energy photon), the energy of the photon is:

\[ E = E_1 - E_2 = -\frac{13.6 \, \text{eV}}{1^2} - \left(-\frac{13.6 \, \text{eV}}{2^2}\right) \]
\[ E = -13.6 \, \text{eV} + \frac{13.6}{4} \]
\[ E = -13.6 + 3.4 = -10.2 \, \text{eV} \]

However, since we are interested in the energy of the photon emitted, we can directly take the energy of the photon corresponding to the transition from \( n = 2 \) to \( n = 1 \):

\[ E = 10.2 \, \text{eV} \]

### Step 2: Work function of cesium
The work function \( \phi \) of cesium is given as \( 1.9 \, \text{eV} \).

### Step 3: Calculate the maximum kinetic energy
Now we can substitute the values into the Einstein photoelectric equation:

\[ K.E. = E - \phi \]
\[ K.E. = 10.2 \, \text{eV} - 1.9 \, \text{eV} \]
\[ K.E. = 8.3 \, \text{eV} \]

### Final Answer
The maximum possible kinetic energy of the photoelectron is \( 8.3 \, \text{eV} \).

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