Question

Rotating Nucleus

According to a crude model, the ⁷Li nucleus is a uniform solid sphere of mass 1.16×10^-26kg and radius 2.30×10^-15m which spins about its diameter. The angular momentum of this spinning lithium nucleus is 1.58×10^-34J ·s. According to this model, what is the angular velocity of the lithium nucleus?
6.44×10²¹ rad/s

¡Correcto! Su recibo es 160-656

Intentos Anteriores

What is the linear velocity of a point on its equator? (Aside: Compare your result to the speed of light, c = 3.00×10⁸m/s)
1.48×10⁷ m/s

¡Correcto! Su recibo es 160-6416

Intentos Anteriores

What is the rotational kinetic energy?
5.09×10^-13 J

¡Correcto! Su recibo es 160-3712

Intentos Anteriores

What is the ratio of the rotational kinetic energy to the relativistic rest-mass energy? (Note: The relativistic rest-mass energy of any particle is given by Einstein's famous equation E = m ·c², where c = 2.9979×10⁸m/s is the speed of light.)

4.88*10^-12 Is incorrect

Answer 1

Given the mass of the nucleus M = 1.16 x 10-26kg,  radius is R = 2.30 x 10-15m and its angular momentum is L = 1.58 x 10-34Js.

a) If I is the moment of inertia of the nucleus and is the angular velocity, then the angular momentum is given by

Nucleus is a uniform solid sphere. The moment of inertia of a solid sphere about the diameter is,

So the angular velocity of the lithium nucleus is 6.44 x 1021 rad/s.

b) The linear velocity v is given by

So the velocity of a point on the equator of the lithium nucleus is 1.48 x 107 m/s.

Given the velocity of light c = 3 x 108 m/s. Comparing v with c, we get

c) The rotational kinetic energy is given by,

So the rotational kinetic energy of the lithium nucleus is 5.09 x 10-13J.

d) Given the velocity of light c = 2.9979 x 108 m/s. The relativistic rest-mass energyis given by

The ratio of rotational kinetic energy to relativistic rest mass energy is,

So the ratio of rotational kinetic energy to relativistic rest mass energy is 4.86 x 10-4.