sbscx28
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A sample of the element Q consists of several isotopes. All of the Q+ ions in the sample of Q that has been ionised in a TOF mass spectrometer have the same kinetic energy.
kinetic energy of each ion = 1/2 mv^2

where m is the mass, in kg, of one ion of an isotope
and v is the velocity of an ion in m s–1 v = dt

where d is the length, in m, of the flight tube
and t is the time taken, in s, for an ion to reach the detector

The time of flight of a 82Q+ ion is 1.243 × 10–5 s. Calculate the time of flight of the 86Q+ ion.
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charco
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(Original post by sbscx28)
A sample of the element Q consists of several isotopes. All of the Q+ ions in the sample of Q that has been ionised in a TOF mass spectrometer have the same kinetic energy.
kinetic energy of each ion = 1/2 mv^2

where m is the mass, in kg, of one ion of an isotope
and v is the velocity of an ion in m s–1 v = dt

where d is the length, in m, of the flight tube
and t is the time taken, in s, for an ion to reach the detector

The time of flight of a 82Q+ ion is 1.243 × 10–5 s. Calculate the time of flight of the 86Q+ ion.
.. and how far have you got?
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Rexx18
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(Original post by sbscx28)
A sample of the element Q consists of several isotopes. All of the Q+ ions in the sample of Q that has been ionised in a TOF mass spectrometer have the same kinetic energy.
kinetic energy of each ion = 1/2 mv^2

where m is the mass, in kg, of one ion of an isotope
and v is the velocity of an ion in m s–1 v = dt

where d is the length, in m, of the flight tube
and t is the time taken, in s, for an ion to reach the detector

The time of flight of a 82Q+ ion is 1.243 × 10–5 s. Calculate the time of flight of the 86Q+ ion.
Put v = d/t into 0.5mv2

Sub in the numbers for the 82 ion to form equation 1.
Sub in the numbers for the 86 ion to form equation 2.
Equate the equations.

The d2 will cancel out.

Re-arrange for t2 and take the square root.

Alternatively, you could give KE a value, such as 1, since both ions will have the same amount of kinetic energy. From this, you'd be able to work out d and then the time for the 86 ion, however, this is more work.
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sbscx28
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(Original post by charco)
.. and how far have you got?
Not very :/ I know that KE is the same and I can substitute d/t over v
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Swissblade
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The two isotopes have the same kinetic energies.

\frac{1}{2}mv^2 = \frac{1}{2}mv^2

Substitute v = \frac{d}{t}

\frac{1}{2}m(\frac{d}{t})^2 = \frac{1}{2}m(\frac{d}{t})^2

Cancel whatever else you can (they both travel the same distance), substitute whatever values you do have and rearrange for relevant t.
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Juliakinga
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How would you get rid of t2?
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