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 8.00×10−13J, and the masses of the helium and gold nuclei were 6.68×10−27kg and 3.29×10−25kg, respectively (note that their mass ratio is 4 to 197). (a) If a helium nucleus scatters to an angle of 120º during an elastic collision with a gold nucleus, calculate the helium nucleus’s final speed and the final velocity (magnitude and direction) of the gold nucleus. (b) What is the final kinetic energy of the helium nucleus?

Q: 5. Show that the kinetic energy of a particle of mass m is related to the momentum p of that…

A: We can express kinetic energy as -  KE=12mv2 .....(1) Where,  m = Mass of the object  v = Velocity…

Q: The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C (mass 2.34 x 10-26…

A:

Q: Osmium (the densest metal found on the periodic table) has a mass density, ρo = 22,500 kg/m3 when…

A:

Q: Consider the following statement: “The concept is particularly important when there is interaction…

A: let force on particle 1 be F1 and force on particle 2 be F2 according to newton's third law F1=-F2…

Q: Find the momentum (in kg. m/s) of a helium nucleus having a mass of 6.68 x 10-27 kg that is moving…

A: Given:-  The mass of the helium nucleus is m = 6.68 x 10-27 kg  The nucleus moves with the velocity…

Q: If a massless particle has momentum 1,368 MeV/c, calculate its energy in MeV.

A:

Q: How much energy is contained in particle with a mass of m= 1 x 10 kg? O 9 × 1033 J O 9 x 10¹6 J O 3…

A: The mass of the particle is given as m=1×10-9 kg

Q: Problem 7: A small block of mass M = 450 g is placed on top of a larger block of mass 3M which is…

A:

Q: Two objects of the same mass move along the same line in opposite directions. The first mass is…

A: Given that,            Two object of same mass, let mass be 'm' each.             moving along…

Q: You are at the controls of a particle accelerator, sending a beam of 1.50 x 107 m/s protons (mass m)…

A: Given, Vp1=1.50×10^7m/s Vp2=1.20×10^7m/s

Q: Is this situation possible? If not, why not? A stationary particle fragments into two particles. One…

A: This situation is not possible.

Q: Suppose a photon, proton, and electron all have the same total energy E. Rank the magnitude of their…

A: Formula to find the relativistic momentum is, Since, the energy and speed of light is constant, p…

Q: Consider a self-gravitating collection of particles. In such a situation, the mean kinetic energy of…

A:

Q: An important fusion reaction in both hydrogen bombs and controlled-fusion reactors is the “DT…

A: The DT reaction is given by

Q: You are at the controls of a particle accelerator, sending a beam of 2.70×107 m/s protons (mass m )…

A: The expression from conservation of momentum,

Q: A proton of mass 1.6 x 10-" kg travelling with a velocity of 3 x 10°ms' collides with a nucleus of…

A:

Q: Why it is necessary to consider that mass of a particle is a function of its velocity?

A:

Q: Find the speed of the electron. Answer in c (b) How would your result change if the particle were a…

A: An electron has momentum with magnitude four times the magnitude of its classical momentum. Find:-…

Q: An electron has a momentum that is 60% larger than its classical momentum. Find the speed of the…

A: Known data: Mass of an electron, m=9.1×10-31kg

Q: The special theory of relativity predicts that there is an upper limit to the speed of a particle.…

A: Special theory of relativity explains how the space and time are linked for objects that are moving…

Q: As part of his discovery of the neutron in 1932, James Chadwick determined the mass of the newly…

A: Let mn and vn be the mass and speed of the neutrons. Consider elastic collision, then

Q: An open system is one in which...... O Mass crosses the boundary but not the energy Neither mass nor…

A: Given : Type of system: An open system

Q: An electron has a momentum that is four times larger than its classical momentum. Find the speed

A: Give An electron has a momentum that is four times larger than its classical momentum. .γ   is the…

Q: In the nuclear fission of a 238U nucleus, "fast" neutrons are emitted with a speed of 0.6497c.…

A: Speed of fast neutron (v) = 0.6497 c Where " c" is the speed of light

Q: A subatomic particle A decays into two identical particles B, A=B + B particles. The two B are…

A: Answer i) zero ii) 2√[moB^2+(PB/c) ^2]

Q: An electron is emitted in beta decay of radioactive caesium It has mass 9.109X10^-31.   and is…

A: Mass of electron m=9.109*10-31kg, velocity of the electron after emission from beta source v=0.75c…

Q: ) A proton (p) of mass 1.43-u(unified atomic mass units) traveling with a speed 4.13 x 104 m/s of…

A:

Q: PHYS-91; Multiple Choice: A 10 kilogram ball falls from a height of 5 meters and rebounds from the…

A: Given data:  Mass (m) = 10 kg Initial height = 5 m Final height = 3 m Required: Loss in energy

Q: A proton of mass 1.6 x 10 " kg travelling with a velocity of 3 x 10'ms' collides with a nucleus of…

A: Here there is elastic collision so linear momentam as well as KE is conserved. So we have.

Q: What is the ratio of the velocity of a β particle to that of an α particle, if they have the same…

A:

Q: During all collisions and explosions, what is conserved?

A:

Q: A particle has y=15,687. Calculate c-v in m/s. (I would have asked for 1- v/c, making the answer…

A: The formula for the gamma is:

Q: Show that the kinetic energy of a particle of mass m is related to the momentum p of that particle…

A:

Q: An electron has a momentum with magnitude four times the magnitude of its classical momentum. (a)…

A: Given:-                 An electron has a momentum with magnitude four times the magnitude of its…

Q: Consider a wood burning fireplace as a system in which the wood is completely burned into ash and…

A: According to the conservation of energy, energy can never be created nor destroyed. Energy can only…

Q: Two particles of mass m and velocity v collide with each other completely inelastic. What is the…

A:

Q: Since the heavy particle remains fixed, before and after the motion of the lighter particle, it does…

A: From the energy conservation, we conclude,…

Q: An unstable particle of mass 3.34 x 10-27 kg is  initially at rest. The particle decays into two…

A: Given: Mass of the parent unstable particle: Velocity of the particle moving toward the left:…

Q: A body of rest mass m and velocity v (and gamma factor y) collides with an identical body at rest.…

A:

Q: During a routine flight in 1956, test pilot Tom Attridge put his jet fighter into a 20 dive for a…

A:

Q: Are the follwing precise, accurate, both or neither for a target of 12.0? a. 11.9 cm, 11.7cm, 12.2…

A: Given: Target 12.0

Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.