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Answer :
Final answer:
The wavelength of an electron can be calculated using the de Broglie equation λ = h / (mv), where h is Planck's constant, m is the mass of the electron, and v is the velocity.
Explanation:
Calculating the Wavelength of an Electron
To determine the wavelength of an electron, we use the de Broglie equation which relates the particle's wavelength to its momentum. The de Broglie wavelength equation is expressed as λ = h / (mv), where:
- λ is the wavelength of the particle,
- h is Planck's constant (6.62607015 × 10-34 m·s),
- m is the mass of the particle (for an electron, 9.10938356 × 10-31 kg), and
- v is the velocity of the particle.
Given the electron's velocity of 1.70×106 m/s, we can calculate its wavelength as follows:
- First, plug in the given values into the de Broglie equation: λ = (6.62607015 × 10-34) / (9.10938356 × 10-31 kg × 1.70×106 m/s).
- Carry out the multiplication in the denominator: (9.10938356 × 10-31 kg) × (1.70×106 m/s) = 1.5486×10-24 kg·m/s.
- Divide Planck's constant by the product to find the wavelength: λ = (6.62607015 × 10-34) / (1.5486×10-24 kg·m/s).
- Calculate the quotient to find λ, the wavelength of the electron, which will be in meters.
Following this process will yield the wavelength of the electron in the ground state of the hydrogen atom.
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