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lara [203]
3 years ago
5

You are at the controls of a particle accelerator, sending a beam of 2.10×107 m/s protons (mass m) at a gas target of an unknown

element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 1.80×107 m/s. Assume that the initial speed of the target nucleus is negligible and the collision is elastic.
A) Find the mass of one nucleus of the unknown element.
B) What is the speed of the unknown nucleus immediately after such a collision?
Physics
1 answer:
Kipish [7]3 years ago
7 0

Answer:

a

The mass is  m_2 =21.75*10^{-27} \ kg

b

The velocity is  v_2 = 3.0*10^{6} m/s

Explanation:

From the question we are told that

     The speed of the protons is  u_1 =  2.10*10^{7} m/s

     The mass of the protons is  m

     The speed of the rebounding protons are v_1 =  -1.80 * 10^{7} \ m/s

The negative sign shows that it is moving in the opposite direction

     

Now according to the law of energy conservation mass of one nucleus of the unknown element. is mathematically represented as

        m_2 = [\frac{u_1 -v_1}{u_1 + v_1} ] m_1

Where m_1 is the mass of a single proton

          So substituting values

       m_2 = \frac{2.10 *10^{7} - (-1.80 *10^{7})} {(2.10 *10^7) + (-1.80 *10^{7})} m_1

        m_2 =13 m_1

The mass of on proton is  m_1 = 1.673 * 10^{-27} \ kg

So     m_2 =13 ( 1.673 * 10^{-27} )

        m_2 =21.75*10^{-27} \ kg

Now according to the law of linear momentum conservation the speed of the unknown nucleus immediately after such a collision is mathematically evaluated as

      m_1 u_1 + m_2u_2 = m_1 v_1 + m_2v_2

Now  u_2 because before collision the the nucleus was at rest

So

        m_1 u_1 =  m_1 v_1 + m_2v_2

=>    v_2 =  \frac{m_1(u_1 -v_1)}{m_2}

Recall that m_2 =13 m_1

So

       v_2 =  \frac{m_1(u_1 -v_1)}{13m_1}

=>         v_2 =  \frac{(u_1 -v_1)}{13}

substituting values

              v_2 =  \frac{( 2.10*10^{7} -(-1.80 *10^{7}))}{13}

              v_2 = 3.0*10^{6} m/s

   

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