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Consider an electron, a proton, and an alpha particle (a helium nucleus), each trapped separately in identical boxes. Which particle has the longest wavelength when the system is in the ground state?

Respuesta :

Answer:

electron

Explanation:

The energy for particle in a box is given by:

[tex]E=\frac{n^2 h^2}{8mL^2}[/tex]

for the system in ground state, n =1

Since, the boxes are identical, L is same for all the three particles.

h is Planck's constant.

Since energy is inversely proportional to wavelength, therefore

[tex]\lambda \propto m[/tex]

[tex]m_e<m_p<m_\alpha[/tex]

[tex]\Rightarrow \lambda_e<\lambda_p<\lambda_\alpha[/tex]

Thus, electron has the longest wavelength.

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