TIME-OF-FLIGHT

The 'Time of flight' (TOF) method of measuring particle mass-to-charge ratio is done as follows.^[1] An ion of known electrical charge and unknown mass enters a mass spectrometer and is accelerated by an electrical field of known strength. This acceleration results in an ion having the same kinetic energy as any other ion that has the same charge. The velocity of the ion will depend however on the mass-to-charge ratio.
The time that it subsequently takes for the particle to reach a detector at a known distance is measured. This time will depend on the mass-to-charge ratio of the particle (heavier particles reach lower speeds). From this time and the known experimental parameters one can find the mass-to-charge ratio of the particle. This method of analysis is a powerful tool for finding the mass-to-charge ratio of charged particles, atoms and molecules.
In near infrared spectroscopy 'Time of Flight' method is used to estimate the wavelength dependent optical pathlength.
In Ultrasonic Flow Measurement, the principle is used to work out speed of signal propagation upstream and downstream of flow, in order to estimate total flow velocity.
In kinematics, TOF is the duration in which a projectile is travelling through the air. Given the initial velocity $u$ of the particle, the downward (i.e. gravitational) acceleration $a$, and the projectile's angle of projection θ (measured relative to the horizontal), then a simple rearrangement of the SUVAT equation s=ut+1/2at² results in this equation for the 'time of flight' of a projectile: t=2$u$(Sin θ)/$|a|$.

Contents

Fundamental Theory

Delayed Extraction

Reflectron TOF

Time-of-flight mass spectrometers in chemistry

High-precision measurements in physics

External links

References

Fundamental Theory

It is well understood in physics that the potential energy of a charged particle in an electric field is related to its charge and to the strength of the electric field:
:$E\_\{p\}\; =\; qU,$ [1]
where ''E_p'' is potential energy, ''q'' is the charge of the particle, and ''U'' is the electric potential difference (also known as voltage).
When the charged particle is accelerated into time-of-flight tube by the voltage ''U'', its potential energy is converted to kinetic energy. The kinetic energy of any mass is:
: [2]
In effect, the potential energy is converted to kinetic energy, meaning that equations [1] and [2] are equal
:$E\_\{p\}\; =\; E\_\{k\},$ [3]
: [4]
The velocity of the charged particle after acceleration will not change since it moves in a field-free time-of-flight tube. The velocity of the particle can be determined in a time-of-flight tube since the length of the path (''d'') of the flight of the ion is known and the time of the flight of the ion (''t'') can be measured using very sophisticated electronic stopwatch technology under the control of a crystal that oscillates at a frequency in the gigahertz range (and thus whose period is thus in the nanosecond range).
Thus,
: [5]
and we substitute the value of ''v'' in Eqn [5] into Eqn [4].
:
ight)^{2}, [6]
Re-arranging Eqn [6] so that the flight time is expressed by everything else:
: [7]
Taking the square root of the time
: [8]
These factors for the time of flight have been grouped purposely. contains constants that in principle do not change when a set of ions are analyzed in a single pulse of acceleration. Eqn 8 can thus be given as:
: [9]
where ''k'' is a proportionality constant representing factors related to the instrument settings and characteristics.
Eqn [9] reveals more clearly that the time of flight of the ion varies with the square root of its mass-to-charge ratio (''m/q'').
Consider a real world example of a MALDI ToF MS instrument which is used to produce a mass spectrum of the tryptic peptides of a protein. Suppose the mass of one tryptic peptide is 1000 daltons (Da). The kind of ionization of peptides produced by MALDI is typically +1 ions, so ''q'' = e in both cases. Suppose the instrument is set to accelerate the ions in a U = 15'000