A moving particle is associated with wavelength `5xx10^(-8) m`. If its momentum is reduced to half of its value compute the new wavelength. If answer is `10^(-x)` then find 'x'.

Explanation

To solve the problem step by step, we will use the relationship between the momentum of a particle and its wavelength, as described by the de Broglie hypothesis.

### Step 1: Understand the relationship between wavelength and momentum
The de Broglie wavelength (λ) of a particle is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant and \(p\) is the momentum of the particle.

### Step 2: Identify the initial conditions
We are given the initial wavelength:
\[ \lambda_1 = 5 \times 10^{-8} \, \text{m} \]
Let the initial momentum be \(p_1\).

### Step 3: Express the initial momentum in terms of wavelength
From the de Broglie equation, we can express the initial momentum as:
\[ p_1 = \frac{h}{\lambda_1} \]

### Step 4: Determine the new momentum
According to the problem, the momentum is reduced to half:
\[ p_2 = \frac{1}{2} p_1 \]

### Step 5: Relate the new wavelength to the new momentum
Using the de Broglie equation again for the new momentum:
\[ \lambda_2 = \frac{h}{p_2} \]
Substituting \(p_2\):
\[ \lambda_2 = \frac{h}{\frac{1}{2} p_1} = \frac{2h}{p_1} \]

### Step 6: Substitute the expression for \(p_1\)
Now, substitute \(p_1\) from Step 3 into the equation for \(\lambda_2\):
\[ \lambda_2 = \frac{2h}{\frac{h}{\lambda_1}} = 2 \lambda_1 \]

### Step 7: Calculate the new wavelength
Now substitute the value of \(\lambda_1\):
\[ \lambda_2 = 2 \times (5 \times 10^{-8}) = 10 \times 10^{-8} = 1 \times 10^{-7} \, \text{m} \]

### Step 8: Express the new wavelength in the required form
The problem states that if the answer is \(10^{-x}\), we can express:
\[ \lambda_2 = 10^{-7} \, \text{m} \]
Thus, comparing this with \(10^{-x}\), we find:
\[ x = 7 \]

### Final Answer
The value of \(x\) is:
\[ \boxed{7} \]