Find the minimum frequency of light which can ionise a hydrogen atom.

Options

A. `3.28xx10^(15)Hz`
B. `5xx10^(15)Hz`
C. 91.1 Hz
D. None of these

Answer

To find the minimum frequency of light that can ionize a hydrogen atom, we will follow these steps:

### Step 1: Understand the energy required for ionization
The energy required to ionize a hydrogen atom is given as 13.6 electron volts (eV).

### Step 2: Convert energy from electron volts to joules
We need to convert the energy from electron volts to joules because the Planck's constant is in joules. The conversion factor is:
1 eV = \(1.6 \times 10^{-19}\) joules.

So, the energy in joules is:
\[ E = 13.6 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 2.176 \times 10^{-18} \, \text{J} \]

### Step 3: Use the formula relating energy and frequency
The energy of a photon is given by the equation:
\[ E = h \mu \]
where:
- \(E\) is the energy in joules,
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{J s}\)),
- \(\mu\) is the frequency in hertz (Hz).

### Step 4: Solve for the minimum frequency
Rearranging the formula to solve for frequency gives:
\[ \mu = \frac{E}{h} \]

Substituting the values we have:
\[ \mu = \frac{2.176 \times 10^{-18} \, \text{J}}{6.63 \times 10^{-34} \, \text{J s}} \]

### Step 5: Calculate the frequency
Calculating this gives:
\[ \mu \approx 3.28 \times 10^{15} \, \text{Hz} \]

### Conclusion
The minimum frequency of light required to ionize a hydrogen atom is approximately \(3.28 \times 10^{15} \, \text{Hz}\).

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