Final answer:
The time it takes for an ion to travel in a mass spectrometer is proportional to the square root of its mass. Since the 81Br ion takes 2.83x10^-5 seconds, we can calculate the time for a 79Br ion using this inverse square root relationship, which is t' = t (sqrt(79) / sqrt(81)).
Step-by-step explanation:
The question concerns the time it takes for different isotopes of bromine to travel along the flight tube in a time-of-flight mass spectrometer under the same conditions. In a time-of-flight (TOF) mass spectrometer, the time is measured for ions to travel a fixed distance. Since the 81Br ion takes 2.83x10-5 seconds to travel down the flight tube, we can use the relationship between mass and time of flight to determine the time for the 79Br ion to travel the same distance.
The key principle at play here is that, under the same conditions, the time of flight for ions in a mass spectrometer is proportional to the square root of their masses (assuming they are singly charged). That is:
t √ᵻ / t' = √ᵰ3 / ᵰ3' where:
- t is the time it takes for the 81Br ion to travel,
- t' is the unknown time for the 79Br ion,
- ᵰ3 is the mass of the 81Br ion, and
- ᵰ3' is the mass of the 79Br ion.
Given that the masses of 81Br and 79Br are 81 amu and 79 amu respectively, we can set up a simple ratio:
t' = t (√ᵰ3' / √ᵰ3) = (2.83x10-5 seconds) (√79 / √81)
Calculating this gives us the time it would take the 79Br ion to travel down the same flight tube.