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What is the de Broglie wavelength of an electron moving at [tex]1.37 \times 10^6 \, \text{m/s}[/tex] if the mass of the electron is [tex]9.11 \times 10^{-28} \, \text{g}[/tex]?

Answer :

Answer:

The value is [tex]\lambda = 5.30 *10^{-10 } \ m[/tex]

Explanation:

From the question we are told that

The velocity of the electron is [tex]v = 1.37 *10^{6} \ m/s[/tex]

The mass of the electron is [tex]m = 9.11 *10^{-28} \ g = 9.11 *10^{-31} \ kg[/tex]

Generally the deBroglie wavelength is mathematically represented as

[tex]\lambda = \frac{h}{mv}[/tex]

Here h is the Planck'c constant with value [tex]h = 6.62607015 * 10^{-34} J \cdot s[/tex]

So

[tex]\lambda = \frac{6.62607015 * 10^{-34} }{9.11 *10^{-31} * 1.37 *10^{6}}[/tex]

=> [tex]\lambda = 5.30 *10^{-10 } \ m[/tex]

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Rewritten by : Barada

The de Broglie wavelength of an electron moving at 1.37 x 10⁶ m/s is calculated to be approximately 5.29 x 10⁻¹⁰ meters using de Broglie's equation. Planck's constant and the mass of the electron are used in the formula to find the wavelength.

The de Broglie wavelength of an electron can be calculated using de Broglie's equation:

λ = h / mv

where λ is the wavelength, h is Planck's constant (6.626 x 10⁻³⁴ J·s), m is the electron's mass, and v is the velocity. Given:

Velocity,

v = 1.37 x 10⁶ m/s

Mass, m = 9.11 x 10⁻²⁸ g = 9.11 x 10⁻³¹ kg (convert grams to kilograms)

Using the formula, we have:

λ = 6.626 x 10⁻³⁴ J·s / (9.11 x 10⁻³¹ kg * 1.37 x 10⁶ m/s)

Simplifying gives:

λ ≈ 5.29 x 10⁻¹⁰ meters

Thus, the de Broglie wavelength of the electron is approximately 5.29 x 10⁻¹⁰ meters.