Question

In order to investigate the structure of atoms, Ernest Rutherford performed his famous experiment, in which...

In order to investigate the structure of atoms, Ernest Rutherford performed his famous experiment, in which he bombarded gold atoms with alpha particles and studied the scattering of the alpha particles. Imagine that an alpha particle (a helium nucleus, consisting of two protons and two neutrons) is initially moving along the x-axis in the positive direction straight toward an initially stationary gold nucleus (containing 79 protons and 118 neutrons) and all subsequent motion takes place along the x-axis. The alpha particle starts with kinetic energy of 9.7 MeV (= 9.7 × 106 eV) far from the gold nucleus. Take the mass of a nucleon (a proton or a neutron) to be 1.7 × 10-27 kg and assume that the mass of a nucleus equals the sum of the masses of its constituent nucleons. Assume also that all speeds are low compared to the speed of light.

50% Part (a) Find the final momentum of the alpha particle (with its sign), long after it interacts with the gold nucleus, in units of kg⋅m/s.

50% Part (b)  Find the final momentum of the gold nucleus (with its sign), long after in interacts with the alpha particle, in units of kg⋅m/s.

Homework Answers

Answer #1

let m1 = 4*m
KE1 = (1/2)*m1*u1^2

u1 = sqrt(2*KE1/m1)

= sqrt(2*9.7*10^6*1.6*10^-19/(4*1.7*10-27))

= 2.136*10^7 m/s

m2 = 197*m
u2 = 0

a) speed of alfa particle after the collision,

v1 = (m1 - m2)*u1/(m1 + m2)

= (4*m - 197*m)*2.136*10^7/(4*m + 197*m)

= -2.05*10^7 m/s

momentum of alfa particle, P1f = m1*v1

= 4*m*v1

= 4*1.7*10^-27*(-2.05*10^7)

= -1.4*10^-19 kg.m/s   <<<<<<<<<<<<---------------------Answer


b) speed of gold nucleus after the collision,

v2 = 2*m1*u1/(m1 + m2)

= 2*4*m*2.136*10^7/(4*m + 197*m)

= 8.50*10^5 m/s

momentum of gold nucleus, P2f = m2*v2

= 197*m*v2

= 197*1.7*10^-27*8.5*10^5

= 2.8*10^-19 kg.m/s <<<<<<<<<<<<---------------------Answer

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In order to investigate the structure of atoms, Ernest Rutherford performed his famous experiment, in which...
In order to investigate the structure of atoms, Ernest Rutherford performed his famous experiment, in which he bombarded gold atoms with alpha particles and studied the scattering of the alpha particles. Imagine that an alpha particle (a helium nucleus, consisting of two protons and two neutrons) is initially moving along the x-axis in the positive direction straight toward an initially stationary gold nucleus (containing 79 protons and 118 neutrons) and all subsequent motion takes place along the x-axis. The alpha...
In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they...
In 1911, Ernest Rutherford and his assistants Geiger and Marsden conducted an experiment in which they scattered alpha particles (nuclei of helium atoms) from thin sheets of gold. An alpha particle, having charge +2e and mass 6.64 x 10-27 kg, is a product of certain radioactive decays. The results of the experiment led Rutherford to the idea that most of the atom’s mass is in a very small nucleus, with electrons in orbit around it. (This is the planetary classic...
During 1910-1911, Sir Ernest Rutherford performed a series of experiments to determine the structure of the...
During 1910-1911, Sir Ernest Rutherford performed a series of experiments to determine the structure of the atom. He aimed a beam of alpha particles (helium nuclei, of mass 6.65×10−27 kg ) at an extremely thin sheet of gold foil. Most of the alphas went right through with little deflection, but a small percentage bounced directly back. These results told him that the atom must be mostly empty space with an extremely small nucleus. The alpha particles that bounced back must...
Rutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An...
Rutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0°; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 1.6 ✕ 107 m/s and a mass of 6.7 ✕ 10−27 kg. Assume the alpha particle collided with a gold nucleus that was initially at rest. Find the speed of the nucleus after the collision.
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that...
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.71 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the...
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that...
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.59 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the...
Ernest Rutherford demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from...
Ernest Rutherford demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 (197Au). The energy of the incoming helium nucleus was 7.10 x 10-13 J, and the masses of the helium and gold nuclei were 6.68 x 10-27 and 3.29 x 10-25 kg, respectively (note that their mass ratio is 4 to 197). A helium nucleus scatters backward to an angle of 120° as measured from its original path during an elastic collision with a...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT