Two H atoms in the ground state collide in elastically. The maximum amount by which their combined kinetic energy is reduced is

Options

A. `10.20 eV`
B. `20.40 eV`
C. `13.6 eV`
D. `27.2 eV`

Explanation

To solve the problem of how much the combined kinetic energy of two hydrogen atoms in the ground state is reduced after an inelastic collision, we can follow these steps:

### Step 1: Determine the initial total energy of the hydrogen atoms.
Each hydrogen atom in the ground state has an energy of -13.6 eV. Therefore, for two hydrogen atoms:

\[ \text{Initial Total Energy} = 2 \times (-13.6 \, \text{eV}) = -27.2 \, \text{eV} \]

### Step 2: Understand the inelastic collision and the excited state.
In an inelastic collision, one of the hydrogen atoms can be excited to a higher energy level (n=2). The energy of the excited state (n=2) for hydrogen is given by:

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

For n=2:

\[ E_2 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]

### Step 3: Calculate the total energy after the collision.
After the collision, one hydrogen atom is in the excited state (n=2) and the other remains in the ground state (n=1). Therefore, the total energy after the collision is:

\[ \text{Total Energy After Collision} = E_2 + E_1 = -3.4 \, \text{eV} + (-13.6 \, \text{eV}) = -17 \, \text{eV} \]

### Step 4: Calculate the reduction in kinetic energy.
The reduction in kinetic energy due to the inelastic collision is the difference between the initial total energy and the total energy after the collision:

\[ \text{Reduction in Kinetic Energy} = \text{Initial Total Energy} - \text{Total Energy After Collision} \]

Substituting the values:

\[ \text{Reduction in Kinetic Energy} = (-27.2 \, \text{eV}) - (-17 \, \text{eV}) = -27.2 \, \text{eV} + 17 \, \text{eV} = -10.2 \, \text{eV} \]

Thus, the maximum amount by which their combined kinetic energy is reduced is:

\[ \text{Reduction in Kinetic Energy} = 10.2 \, \text{eV} \]

### Final Answer:
The maximum amount by which their combined kinetic energy is reduced is **10.2 eV**.

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