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Find the mass of a particle with a Compton wavelength of πrS where rS is the Schwarzschild radius. This mass is called the Planck mass mP, and the energy required to create the mass is called the Planck energy EP = mPc2. Determine the values of both the Planck mass and energy.

Find the mass of a particle with a Compton wavelength of πrS where rS is the Schwarzschild radius. This mass is called the Planck mass mP, and the energy required to create the mass is called the Planck energy EP = mPc2. Determine the values of both the Planck mass and energy.

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Find the mass of a particle with a Compton wavelength of πrS where rS is the Schwarzschild radius. This mass is called the Planck mass mP, and the energy required to create the mass is called the Planck energy EP = mPc2. Determine the values of both the Planck mass and energy.

Expert Solution
Step 1

We know,

Schwarzschild radius, rs=2Gmc2

Gravitational constant, G=6.67×10-11 Nm2kg2

Compton wavelength, λc=hmc

Here,

h is the Planck's constant=6.63×10-34 Js

Step 2

According to question,

2Gmc2=hmc⇒m2=hc2G⇒m=6.63×10-34×3×1082×6.67×10-11=0.386×10-7 kg

Thus Planck's mass, mP=0.386×10-7 kg

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