To better understand the Earth's climate history, you are using a mass spectrometer to distinguish different isotopes of oxygen in an ice core sample from an old glacier. The various isotopes are all moving at v = 4.9 × 106 m/s when they enter a chamber containing a uniform magnetic field B = 1.2 T. The isotope that is currently entering the detector is singly-ionized oxygen-16, with a mass of m = 2.66×10-26 kg and a charge of te. 74.127.87.86 Beam of oxygen atoms Detector D B Do all of the following: • a) Write down an algebraic equation for the diameter D of the charged particle's circular path in a magnetic field. If necessary, you may derive the equation starting from Newton's 2nd Law with centripetal acceleration. Include the equation in the work you submit in the even-numbered question that follows. • b) Calculate this diameter value for singly-ionized oxygen-16 based on the given values. Enter the numerical value in the box below, with two digits after the decimal, in units of meters. This is the fixed distance between the entry and exit holes in the device shown above. • c) Suppose you want to re-tune the magnetic field so that now oxygen-18 passes into the detector by following the circular path as before. This new isotope is 18/16 = 1.125 times more massive, but the charge and speed are the same as before. What is the new value of the magnetic field that will make that happen? Report the numerical value in the work you submit below. Be sure to include two digits after the decimal, as well as the appropriate units.
To better understand the Earth's climate history, you are using a mass spectrometer to distinguish different isotopes of oxygen in an ice core sample from an old glacier. The various isotopes are all moving at v = 4.9 × 106 m/s when they enter a chamber containing a uniform magnetic field B = 1.2 T. The isotope that is currently entering the detector is singly-ionized oxygen-16, with a mass of m = 2.66×10-26 kg and a charge of te. 74.127.87.86 Beam of oxygen atoms Detector D B Do all of the following: • a) Write down an algebraic equation for the diameter D of the charged particle's circular path in a magnetic field. If necessary, you may derive the equation starting from Newton's 2nd Law with centripetal acceleration. Include the equation in the work you submit in the even-numbered question that follows. • b) Calculate this diameter value for singly-ionized oxygen-16 based on the given values. Enter the numerical value in the box below, with two digits after the decimal, in units of meters. This is the fixed distance between the entry and exit holes in the device shown above. • c) Suppose you want to re-tune the magnetic field so that now oxygen-18 passes into the detector by following the circular path as before. This new isotope is 18/16 = 1.125 times more massive, but the charge and speed are the same as before. What is the new value of the magnetic field that will make that happen? Report the numerical value in the work you submit below. Be sure to include two digits after the decimal, as well as the appropriate units.
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Transcribed Image Text:To better understand the Earth's climate history, you are using a mass spectrometer
to distinguish different isotopes of oxygen in an ice core sample from an old glacier.
The various isotopes are all moving at v = 4.9 × 106 m/s when they enter a
chamber containing a uniform magnetic field B = 1.2 T. The isotope that is
currently entering the detector is singly-ionized oxygen-16, with a mass of m =
2.66x10- -26
kg and a charge of te.
74.127.87.86
1:
Beam of
oxygen atoms
Detector
D
Do all of the following:
• a) Write down an algebraic equation for the diameter D of the charged
particle's circular path in a magnetic field. If necessary, you may derive the
equation starting from Newton's 2nd Law with centripetal acceleration.
Include the equation in the work you submit in the even-numbered question
that follows.
• b) Calculate this diameter value for singly-ionized oxygen-16 based on the
given values. Enter the numerical value in the box below, with two digits after
the decimal, in units of meters. This is the fixed distance between the entry
and exit holes in the device shown above.
• c) Suppose you want to re-tune the magnetic field so that now oxygen-18
passes into the detector by following the circular path as before. This new
isotope is 18/16 = 1.125 times more massive, but the charge and speed are
the same as before. What is the new value of the magnetic field that will make
that happen? Report the numerical value in the work you submit below. Be
sure to include two digits after the decimal, as well as the appropriate units.
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