In Planck's oscillator energy is given as
`E=(hv)/(exp((hv)/(Kt)-1))`
If K=0 , then energy would be

Options

A. hv
B. 0
C. Kt
D. `oo`

Answer

To solve the problem, we start with the given equation for the energy of Planck's oscillator:

\[ E = \frac{h \nu}{\exp\left(\frac{h \nu}{k T}\right) - 1} \]

where:
- \(E\) is the energy,
- \(h\) is Planck's constant,
- \(\nu\) is the frequency,
- \(k\) is the Boltzmann constant,
- \(T\) is the temperature.

We need to find the value of energy \(E\) when \(k = 0\).

### Step 1: Substitute \(k = 0\) into the equation

Substituting \(k = 0\) into the equation gives us:

\[ E = \frac{h \nu}{\exp\left(\frac{h \nu}{0 \cdot T}\right) - 1} \]

### Step 2: Analyze the term \(\frac{h \nu}{0 \cdot T}\)

The term \(\frac{h \nu}{0 \cdot T}\) tends to infinity because division by zero is undefined and leads to an infinite limit. Therefore, we can express this as:

\[ \frac{h \nu}{0 \cdot T} \to \infty \]

### Step 3: Evaluate the exponential function

As \(x\) approaches infinity, \(\exp(x)\) also approaches infinity. Therefore, we have:

\[ \exp\left(\frac{h \nu}{0 \cdot T}\right) \to \infty \]

### Step 4: Substitute back into the energy equation

Now substituting this back into the energy equation, we get:

\[ E = \frac{h \nu}{\infty - 1} \]

Since \(\infty - 1\) is still infinite, we can simplify this to:

\[ E = \frac{h \nu}{\infty} \]

### Step 5: Evaluate the limit

When we divide a finite number by infinity, the result approaches zero:

\[ E \to 0 \]

### Conclusion

Thus, when \(k = 0\), the energy \(E\) approaches zero. Therefore, the final answer is:

\[ E = 0 \]