Natural carbon consists of two different isotopes (excluding l4C, which is prese

Question

Natural carbon consists of two different isotopes (excluding l4C, which is present in only trace amounts). The isotopes have different masses, which is due to different numbers of neutrons in the nucleus; however, the number of protons is the same, and subsequently the chemical properties are the same. The most abundant isotope has an atomic mass of 12.00 u. When natural carbon is placed in a mass spectrometer, two lines are formed on the photographic plate. The lines show that the more abundant isotope moved in a circle of radius 15.0 cm, while the rarer isotope moved in a circle of radius 15.6 cm. What is the atomic mass of the rarer isotope? (The ions have the same charge and are accelerated through the same potential difference before entering the magnetic field.)

Explanation / Answer

The mass of the abundant isotope is m1 = 12 u The radius of the circular path of abundant isotope is R1 = 15 cm The radius of the circular path of rarer isotope is R2 = 15.6 cm As by the definetion of central force, the radius of the path travelled will always proportional to the mass of the particle. m1/m2 = R1/R2 12 u/m2 = 15 cm / 15.6 cm m2 = 12.48 u

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