The ratio of the energies of two different radiation whose frequenceies are `3xx10^(14)`Hz and `5xx10^(14)`Hz is `"____________"`

Answer

To find the ratio of the energies of two different radiations based on their frequencies, we can follow these steps:

### Step-by-Step Solution

1. **Understand the relationship between energy and frequency**: The energy (E) of radiation is given by the formula:
\[ E = h \cdot \nu \]
where \( h \) is Planck's constant and \( \nu \) (mu) is the frequency of the radiation.

2. **Identify the frequencies**: We are given two frequencies:
- \( \nu_1 = 3 \times 10^{14} \) Hz
- \( \nu_2 = 5 \times 10^{14} \) Hz

3. **Write the expressions for energies**: Using the formula for energy, we can write:
- Energy for the first radiation:
\[ E_1 = h \cdot \nu_1 = h \cdot (3 \times 10^{14}) \]
- Energy for the second radiation:
\[ E_2 = h \cdot \nu_2 = h \cdot (5 \times 10^{14}) \]

4. **Set up the ratio of the energies**: We want to find the ratio \( \frac{E_1}{E_2} \):
\[ \frac{E_1}{E_2} = \frac{h \cdot \nu_1}{h \cdot \nu_2} \]

5. **Simplify the ratio**: The Planck's constant \( h \) cancels out:
\[ \frac{E_1}{E_2} = \frac{\nu_1}{\nu_2} = \frac{3 \times 10^{14}}{5 \times 10^{14}} \]

6. **Calculate the ratio**: The \( 10^{14} \) terms also cancel out:
\[ \frac{E_1}{E_2} = \frac{3}{5} \]

### Final Answer
The ratio of the energies of the two different radiations is:
\[ \frac{E_1}{E_2} = \frac{3}{5} \]