Beryllium-8 is an unstable isotope and decays into two α particles, which are helium nuclei with mass 6.68×10−27kg . This decay process releases 1.5×10−14J of energy. For this problem, let's assume that the mass of the Beryllium-8 nucleus is just twice the mass of an α particle and that all the energy released in the decay becomes kinetic energy of the α particles. If a Beryllium-8 nucleus is at rest when it decays, what is the speed of the α particles after they are released?

1498502.2 m/s

Explanation:

mass of the helium =  6.68×10−27kg

energy released during the decay =  1.5×10−14J

since all the energy released is converted to kinetic energy of the alpha particle then particle will have kinetic energy = 0.5 mh v²

1.5×10−14J = 2 ( 0.5 mh v²) where mh is mass of helium

1.5×10−14J  / ( 6.68×10−27kg) = v²

v = 1498502.2 m/s

v = 1498502.2 m/s

Explanation:

All energy that was released is been converted to kinetic energy of the alpha particle, particle having a kinetic energy of = 0.5 mh v²

We are given the following as;

mass of the helium =  6.68×10−27kg

decay process release energy of =  1.5×10−14J

Calculating the speed of alpha particle after the release in this equation, we have

1.5×10−14J = 2 ( 0.5 mh v²)

Substituting the value of mh in the equation, we have

v² = 1.5×10−14J  / ( 6.68×10−27kg)

To eliminate the square root, we introduce square root to both sides

√v² = √1.5×10−14J  / ( 6.68×10−27kg)

v= 1498502.2 m/s

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

d is the correct answer