RW22 Name: _________________About this assignmentSections 8.2-8.4(p. 270-276). Question 5 relates to the Rutherford scattering program you wrote in lab.1. Early in Chapter 8 these formulas are derived for the final momenta after a collision of two objects whose masses are M and m:xixfpmmmmp.12121.1 and xixfpmmmp.1212.22Check all the conditions that must be true for these formulas to be valid:a. m2 must be greater than m1b. The initial speed of the moving object must be << cc. The collision must be elasticd. The collision must be head-on (impact parameter = 0)e. The object of mass m2 must be initially at rest2. We can use the textbook results for head-on elastic collisions to analyze the recoil of the Earth when a ball bounces off a wall embedded in the Earth. Suppose a professional baseball pitcher hurls a baseball (m = 155 grams = 0.155 kg) with a speed of 105 miles per hour (vball = 46.2 m/s) at a wall, and the ball bounces back with little loss of kinetic energy.(a) What is the recoil speed of the Earth (m2 = 6 ×1024 kg)?vEarth = ____________________ m/sCalculate the recoil kinetic energy of the Earth and compare to the kinetic energy of the baseball. The Earth gets lots of momentum (twice the momentum of the baseball) but very little kinetic energy.KEarth = _________________ JKbaseball = _______________ J3. In a collision between an electron and a hydrogen atom, it is useful to select both objects as the system because:a. The total momentum of the system does not change during the collisionb. The forces the objects exert on each other are internal to the system and don't change the total momentum of the systemc. The kinetic energy of a two-object system is nearly zerod. During the time interval just before to just after the collision, external forces are negligiblee. The sum of the final kinetic energies must equal the sum of the initial kinetic energies4. You know that a collision must be "elastic" if:a. The momentum of the two-object system doesn't changeb. The sum of the final kinetic energies equals the sum of the initial kinetic energiesc. The colliding objects are stretchy or squishyd. The colliding objects stick togethere. There is no change in the internal energies of the objects (thermal energy, vibrational energy, etc.)5. An alpha particle (a helium nucleus, containing 2 protons and 2 neutrons) starts out with kinetic energy of 9.5 MeV (9.5 106 eV), and heads in the +x direction straight toward a gold nucleus (containing 79 protons and 118 neutrons). The particles are initially far apart. Answer the following questions about the collision.What is the initial momentum of the alpha particle? (You may assume its speed is small compared to the speed of light).ip,= <_____________ , 0, 0 > kg·m/sWhat is the initial momentum of the gold nucleus?pAu,i = <_______ , ________ , _________ > kg·m/sWhat is the final momentum of the alpha particle, long after it interacts with the gold nucleus?p,f = < __________, __________ , ___________ > kg·m/sWhat is the final momentum of the gold nucleus, long after it interacts with the alpha particle?pAu,f = < __________, __________ , ___________ > kg·m/sWhat is the final kinetic energy of the alpha particle?K ,f = __________________ JWhat is the final kinetic energy of the gold nucleus?KAu,f = _________________ JAssuming that the movement of the gold nucleus is negligible, calculate how close the alpha particle will get to the gold nucleus in this head-on collision. (Given the initial kinetic energy & how the potential energy depends upon separation…)rclosest = ________________ mIn the last question above, what principle did you use to calculate the distance of closest approach?a. Both the energy principle and the momentum principleb. No principles needed, just the definition of velocityc. The energy principled. There is not a principle that applies to this situatione. The momentum principleThe radius of the alpha particle is 2 ×10-15 m, and the radius of the gold nucleus is 8 ×10-15 m (see Prob. 4.15 part c on p. 161 of the textbook). At the point of closest approach, do the two particles touch each other?a. Nob. Not enough information to tellc.