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 formula for the energy of a Planck oscillator:

\[ E = \frac{hv}{e^{\frac{hv}{kT}} - 1} \]

We need to analyze the situation when \( k = 0 \).

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

When substituting \( k = 0 \), the term \( \frac{hv}{kT} \) becomes undefined because we cannot divide by zero. However, we can analyze the limit as \( k \) approaches 0.

### Step 2: Analyze the limit as \( k \to 0 \)

As \( k \) approaches 0, the term \( \frac{hv}{kT} \) approaches infinity if \( T \) (temperature) is not zero. Therefore, we can rewrite the expression in the limit form:

\[ \lim_{k \to 0} E = \frac{hv}{e^{\infty} - 1} \]

### Step 3: Evaluate \( e^{\infty} \)

The expression \( e^{\infty} \) tends to infinity. Thus, we have:

\[ e^{\infty} - 1 \approx \infty \]

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

Now substituting this back into the energy equation gives us:

\[ E = \frac{hv}{\infty} \]

### Step 5: Simplify the expression

Since any finite number divided by infinity approaches zero, we conclude that:

\[ E \to 0 \]

### Final Answer

Thus, if \( k = 0 \), the energy \( E \) would be:

\[ E = 0 \]

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