Question

A nitrogen atom of m₁=14 u is moving with an initial kinetic energy K_i and strikes a stationary tungsten atom of m₂=184 u. During the collision, some of the kinetic energy of the incident atom is used to ionize the stationary atom; an energy E is needed to eject one electron. The ejected electron has less than 0.0001 times the mass of the atoms, so it carries away a negligible momentum. After the collision, the two atoms stick together and move off as a diatomic ionized molecule with kinetic energy, K_f. Eventually you will be asked to find the minimum kinetic energy of the incident atom needed to ionize the stationary atom.

20. [1pt]
Select the statements that are true; e.g., if only statements A and B are true, enter AB; if none are true, enter N. You only have 3 tries!

Our professor is crazy to assign such a problem because we have not been taught the material needed to complete it.

If the (initially stationary) atom becomes ionized, then K_i  ≥  K_f+E.

The energy used in the ionization process is analogous to energy stored in a form other than kinetic energy (e.g., as in a compressed spring).

During the collision the linear momentum is conserved.

Answer:  

Answer 1

let m1 = 14*u
m2 = 184*u
let vi is the initial speed of m1.

let vf is the final speed of the combined molecule.

Apply conservation of momentum

final momentum = initial momentum

(m1 + m2)*vf = m1*vi

(14*u + 184*u)*vf = 14*u*vi

vf = vi*14/(14 + 184)

vf = 0.0707*vi

Ki/Kf = (1/2)*m1*vi^2/((1/2)*(m1 + m2)*vf^2)

= 14*vi^2/((14 + 184)*(0.0707*vi)^2)

= 14/(198*0.0707^2)

= 14.1

Ki = 14.1*Kf

20)

If the (initially stationary) atom becomes ionized, then Ki ≥ Kf+E. ---> True

The energy used in the ionization process is analogous to energy stored in a form other than kinetic energy (e.g., as in a compressed spring). ---> False

During the collision the linear momentum is conserved. --> True