Question
A sample of antimony is analysed in a time of flight (TOF)mass spectrometer and is found to contain two isotopes, 121Sb and {}^123Sb After electron impact ionisation all of the ions are accelerated to the same kinetic energy (KE) and then travel through a flight tube that is 1.05 m long. A 121Sb^ast ion takes 5.93times 10^-4s to travel through the flight tube. The kinetic energy of an ion is given by the equation KE=(1)/(2)mv^2 KE=kinetic energy/J m=mass/kg v=speed/ms^-1 Calculate the mass, in kg, of one {}^121Sb^+ ion. Calculate the time taken for a 123Sb^+ ion to travel through the same flight tube. The Avogadro constant, L=6.022times 10^23mol^-1 [5
Answer
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Wesley
Elite · Tutor for 8 years
Answer
To Be Calculated (^Assistant, Please follow Step 1,2,3 to detailly illustrate the calculation proccess here in HTML style.)
Explanation
This question from Physics requires us to employ the formula for kinetic energy and make as a simple calculations based on constants and conditions given in the question.Step 1: To find the mass of one 121Sb^+ ion, we first calculate its speed knowing it's time of flight. Since the distance divided by time equals speed, we already know the distance the ion travelled is 1.05 m and its time of flight (ToF) is 5.93 * 10^-4 s, the velocity will be 1.05/(5.93 * 10^-4)= v. Step 2: Issue the equation for kinetic energy KE=1/2mv^2. As per the question, all the ions are accelerated to the same kinetic energy, so in this scenario, we would consider the ions to have equal kinetic energy which remains constant; it means if we neglect any external effecting factor like other forms of energies, we can only observe variation due to speed and mass within system. Movements between the 'two' will balance each other out.In this context, for a given KE, as mass increases, speed SHOULD decrease and vice versa. As mass decreases, speed will tend to increase. Rearrange the equation m= 2KE/v^2Step 3: To find out how much time it takes for a 123Sb^+ ion to travel through the same flight tube, we again use the traveling velocity we found in step 1, because the same testing procedures within same equipment assure us to accept the argument that both isotopes should gain the same level of kinetic energy from external source (acceleration stage), also ions are under same energy status. Due to the dynamics of Hasel's effect，calculate time using the equation time = distance/speed.