Any help would be much appreciated! Will rate! Nothing to transcribe Electrospra

Question

Any help would be much appreciated! Will rate!

Nothing to transcribe Electrospray mass spectrum of Col E1 plasmid DNA (MW = 7.3 MDa). Data represent over 3000 single-ion measurements recorded over a twenty-minute period. From S.D. Fuerstenau and W.H. Benner, "Molecular Weight Determination of Megadalton DNA Electrospray Ions Using Charge Detection Time-of-flight Mass Spectrometry," Rapid Commun. Mass. Spectrom. 9,1528-38(1995). Mass spectrometry allows one to separate charged particles based on the mass to charge ratio. There are several different approaches for performing mass spectrometric analysis. One approach utilizes crossed electric and magnetic fields to balance the forces on the traveling particle while another approach uses magnetic fields to cause a charged particle to travel through an arc of radius R and onto a detector element The data shown above is based on the former approach and looks at the separation of DNA segments. This approach is referred to as time-of-flight mass spectrometry. This problem will consider the latter technique. For this problem, consider ions of different masses m but the same charge q are accelerated through an electrostatic potential difference V, and then enter perpendicularly into a uniform magnetic field B. Determine an expression for the radius of the orbit of the particle, R, in terms of the known quantities (i.e., m, q, B, V). Show that the fractional difference in radius between two particles of slightly different mass Delta m is given by Delta R/R = 1/2 Delta m/m

Explanation / Answer

a)

conservation of energy:

q V = 0.5 m v^2 ===> v = sqrt(2 q V/m)

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q v B = m v^2/R

==> R = q B/(m v) = q B/(m sqrt(2 q V/m)) = q B/sqrt(2 m q V) = B sqrt(q/(2mV))

b)

dR/dm = B/2 (q/(2 V m^2)) sqrt(2mV/q) = (B/2) (1/m) sqrt(q/(2Vm))

==> dR/R = ((B/2) (1/m) sqrt(q/(2Vm)) dm)/(B sqrt(q/(2mV))) = (1/2) (dm/m)

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