4. A deuteron is a nuclear particle made up of one proton and one neutron. It is

Question

4. A deuteron is a nuclear particle made up of one proton and one neutron. It is a nucleus of hydrogen. Its mass is about 3.4 x 1024 g. A deuteron, accelerated by a cyclotron to a speed of 10* cm/s, collides with another deuteron at rest. a. If the two particles stick together head-on to form a helium nucleus, find the speed of the resulting nucleus 24 b. the helium nucleus then breaks up into a neutron with a mass of about 1.7 x 10 g and a helium isotope of mass 5.1 x 1024 g. If the neutron is given off at right angles to the direction of the original velocity with a speed of 5.0 x 10 cm/s, find the magnitude and direction of the velocity of the helium isotope. 5. A flat piece of wood painted blue of uniform density has the following shape. Where is the center of mass of the object? 20 cm 10 cm 10 cm 15 cm 20 cm

Explanation / Answer

a) Apply conservation of momentum

m1*u1 = (m1 + m2)*v

==> v = m1*u1/(m1+m2)

= 3.4*10^-24*10^8/(2*3.4*10^-24)

= 5*10^7 cm/s

b) Apply consrvation of momentum in x-direction

(m1+m2)*v = m_He*vx

==> vx = (m1 + m2)*v/m_He

= 2*3.4*10^-24*5*10^7/(2*3.4*10^-24 - 1.7*10^-24)

= 6.67*10^7 cm/s

Apply consrvation of momentum in y-direction

m*v' = m_He*vy

vy = m*v'/m_He

= 1.7*5*10^8/5.1

= 1.67*10^8 cm/s

velocity of helium Isotope = sqrt(vx^2 +vy^2)

= sqrt((5*10^7)^2 + (1.67*10^8)^2)

= 1.74*10^8 cm/s <<<<<<<<-----Answer

direction : theta = tan^-1(vy/vx)

= tan^-1(1.67/0.5)

= 73.3 degrees from its original direction <<<<<<<<-----Answer

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