A particle has a velocity that is 92% of the speed of light. If the wavelength of the particle is 1.55×10-15 m, calculate the mass of the particle.
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To calculate the mass of the particle, we can use the relativistic equation:
\( m = \frac{m_0}{\sqrt{(1 - \frac{v^2}{c^2})}} \)
Where:
- m is the relativistic mass of the particle
- m0 is the rest mass of the particle
- v is the velocity of the particle
- c is the speed of light
In this case, we are given that the velocity of the particle is 92% of the speed of light. Therefore, \( v = 0.92c \).
The speed of light, c, is approximately \( 3 \times 10^8 \) meters per second.
Now, we can substitute the given values into the equation to solve for the mass of the particle:
\( m = \frac{m_0}{\sqrt{(1 - \frac{v^2}{c^2})}} \)
\( m = \frac{m_0}{\sqrt{(1 - \frac{(0.92c)^2}{c^2})}} \)
Simplifying the equation:
\( m = \frac{m_0}{\sqrt{(1 - 0.92^2)}} \)
\( m = \frac{m_0}{\sqrt{(1 - 0.8464)}} \)
\( m = \frac{m_0}{\sqrt{(0.1536)}} \)
\( m = \frac{m_0}{0.3916} \)
In order to calculate the mass of the particle, we need to know the rest mass, m0. This value is not provided in the question. The rest mass of a particle is usually given in kg or other appropriate units.
Once you have the rest mass of the particle (m0), you can substitute it into the equation to find the relativistic mass (m).