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MMLU-Pro / 9461 / In an early model of the hydrogen atom (the Bohr model), the electron orbits the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

In an early model of the hydrogen atom (the Bohr model), the electron orbits the proton in uniformly circular motion. The radius of the circle is restricted (quantized) to certain values given by where a0=52.92pma_0=52.92 \mathrm{pm}. What is the speed of the electron if it orbits in the smallest allowed orbit?
Plain-text mathematical notation (without MathML)
In an early model of the hydrogen atom (the Bohr model), the electron orbits the proton in uniformly circular motion. The radius of the circle is restricted (quantized) to certain values given by where a₀=52.92pm. What is the speed of the electron if it orbits in the smallest allowed orbit?
Original LaTeX notation
In an early model of the hydrogen atom (the Bohr model), the electron orbits the proton in uniformly circular motion. The radius of the circle is restricted (quantized) to certain values given by where $a_0=52.92 \mathrm{pm}$. What is the speed of the electron if it orbits in the smallest allowed orbit?

category

physics

options

  1. $2.29 \times 10^6 \, \mathrm{m/s}$
  2. $1.89$$10^6 \mathrm{~m} / \mathrm{s}$
  3. $2.39$$10^6 \mathrm{~m} / \mathrm{s}$
  4. $1.59 \times 10^6 \, \mathrm{m/s}$
  5. $2.09 \times 10^6 \, \mathrm{m/s}$
  6. $2.09$$10^6 \mathrm{~m} / \mathrm{s}$
  7. $1.69 \times 10^6 \, \mathrm{m/s}$
  8. $1.99 \times 10^6 \, \mathrm{m/s}$
  9. $2.49 \times 10^6 \, \mathrm{m/s}$
  10. $2.19$$10^6 \mathrm{~m} / \mathrm{s}$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9461
task_id
695a35a0-d077-53d6-89a3-81e26d1302b2
task_key
default--test--9461
task_revision_id
1
config / split
default / test

Official source

initial import