T7S.2 Imagine that in a certain physics experiment, we have a plasma of ionized

Question

T7S.2 Imagine that in a certain physics experiment, we have a plasma of ionized oxygen atoms emerging from an opening in a furnace with a temperature of 2200K. We then use a velocity selector (such as the one discussed in unit E) which passes only ions within 0.01km/s of 1.9km/s. If we need about 3 × 10 ions per second with the selected speed for our experiment, about how many ions per second must the furnace emit? (We can use this information to help determine what furnace to order.) 12 Ion Emission Rate = Constants used: k, 1.38 × 10-23J/K Morgen = 16.00g/mol Na = 6.02 × 1023m 01-1

Explanation / Answer

This problem can be treated using the distribution law of Maxwell-Boltzmann speed

Nv= 4N (m/2kBT)3/2v2e-A

A = mv2/2kBT

B = 4 (m/2kBT)3/2

Nv = B N v2 e-A

Data

v = 1.9 Km/s = 1.9 103 m/s

T = 2200K

n = 16 g/mol = 16 10-3 Kg/mol

Nv = 3 x 1012 ions/s

Calculate N

N = Nv /B v-2 e A

calculate

n = m mol

m = n / mol

m = 16 10-3 /6.02 1023

m = 2.6578 10-26 Kg

A = 2.6578 10-26 1.9 103 /(2 1.38 10-23 2200)

A = 0.00083166

B = 4 (2.6578 10-26 /2 1.38 10-23 2200)3/2

B= 4 ( 1.39328 10-7)1.5

B = 4 1.644 10-10.5

B = 20.66 10-10.5

Calculate N

N = 3 1012 / (20.66 10-10.51.9 103) e0.00083166

N = 7.649 1017.5

N = 2.4 1018 ions

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