Respuesta :
The work done w in terms of K₁ is (9/16)K₁..Work done is equal to change in kinetic energy of the body.
Since, it is given a electron is moving with Kinetic energy. We know that kinetic energy of any moving body is given by=(1/2)mv²
where m is defined as the mass of the body
and v is defined as the velocity of the body.
Initially K₁.=(1/2)[tex]m_e[/tex]v²
=>v²=2 K₁ / [tex]m_e[/tex]
=>v=√(2 K₁ / [tex]m_e[/tex])--------(eq1)
Now,velocity of body becomes one plus one-fourth of the above velocity,so new velocity is =[√(2 K₁ / [tex]m_e[/tex]) + [(1/4)×√(2 K₁ / [tex]m_e[/tex])]=(5/4)×√(2 K₁ / [tex]m_e[/tex].
Therefore, we know that work done is equal to change in kinetic energy of the body
=>W=(1/2)×[tex]m_e[/tex]×(v₂²-v₁²)
=>W=(1/2)×[tex]m_e[/tex] × ([(5/4)²×√(2 K₁ / [tex]m_e[/tex].)²- (√(2 K₁ / [tex]m_e[/tex]))²]
=>W=(1/2)×[tex]m_e[/tex] ×[(25/16)-1]×(2 K₁ / [tex]m_e[/tex].)
=>W=((25-16)/16)×K₁
=>W=(9/16)×K₁
Hence, work done in terms of K₁ is (9/16)K₁.
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