A mass spectrometer is used to separate two isotopes of uranium with masses m1 a

Question

A mass spectrometer is used to separate two isotopes of uranium with masses m1 and m2 where m2 is greater than m1. The two types of uranium atom exit an ion source S with the same charge of +e and are accelerated through a potential difference V. The charged atoms then enter a constant, uniform magnetic field B as shown. If r = 0.5049 m and r2= 0.5081 m, what is the value of the ratio m1/m2? A mass spectrometer is used to separate two isotopes of uranium with masses m1 and m2 where m2 is greater than m1. The two types of uranium atom exit an ion source S with the same charge of +e and are accelerated through a potential difference V. The charged atoms then enter a constant, uniform magnetic field B as shown. If r = 0.5049 m and r2= 0.5081 m, what is the value of the ratio m1/m2?

Explanation / Answer

Inmagnetic field Bvq = mv^ 2/ r Bq = mv / r charge qis same So, B = mv / r ----( 1) Speed of the isotope when it passes through a potential difference V is v = sqrt ( 2Vq / m) plug it in eq ( 1) we get B = ( m / r) sqrt ( 2Vq / m) = [sqrt m] / r Since V , q is same sqrt ( m ' / m ) = r ' / r ---( 2) Since magnetic field b is same. given r = 0.5049 m and r '= 0.5081 m therefore the value of the ratio m/ m ' = ( r / r' ) ^ 2 Since from eq( 2) = 0.98744

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