Textbook Question
Determine the speed of a 15 MeV helium atom.
25. Electric Potential
The ElectronVolt
Problem 16a
Textbook Question
Express in eV (or keV or MeV if more appropriate): The kinetic energy of an electron moving with a speed of 5.0 x 10⁶ m/s .
Verified step by step guidance1
Step 1: Recall the formula for kinetic energy, which is given by \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the electron and \( v \) is its velocity.
Step 2: Substitute the known values into the formula. The mass of an electron \( m \) is approximately \( 9.11 \times 10^{-31} \; \text{kg} \), and the velocity \( v \) is given as \( 5.0 \times 10^6 \; \text{m/s} \).
Step 3: Calculate the kinetic energy in joules using the formula \( KE = \frac{1}{2}mv^2 \). This involves squaring the velocity, multiplying by the mass, and then dividing by 2.
Step 4: Convert the kinetic energy from joules to electronvolts (eV). Use the conversion factor \( 1 \; \text{eV} = 1.602 \times 10^{-19} \; \text{J} \). Divide the kinetic energy in joules by this factor to express it in eV.
Step 5: If the resulting value is very large or very small, express it in keV (\( 1 \; \text{keV} = 10^3 \; \text{eV} \)) or MeV (\( 1 \; \text{MeV} = 10^6 \; \text{eV} \)) for convenience.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Kinetic Energy
Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v², where m is the mass and v is the velocity of the object. For an electron, this energy can be expressed in electronvolts (eV), a unit commonly used in particle physics to represent small energy values.
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Mass of an Electron
The mass of an electron is approximately 9.11 x 10⁻³¹ kg. This small mass is crucial for calculating the kinetic energy of the electron when it is moving at high speeds, as even small changes in velocity can result in significant changes in kinetic energy due to the squared term in the kinetic energy formula.
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Conversion to Electronvolts
Electronvolts (eV) are a unit of energy defined as the amount of kinetic energy gained by an electron when it is accelerated through an electric potential difference of one volt. To convert kinetic energy from joules to electronvolts, one can use the conversion factor 1 eV = 1.602 x 10⁻¹⁹ joules, allowing for easier interpretation of energy values in the context of atomic and subatomic processes.
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