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MMLU-Pro / 4353 / When alkali metals dissolve in liquid ammonia, their atoms each lose an electron…

Problem

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

question

When alkali metals dissolve in liquid ammonia, their atoms each lose an electron and give rise to a deep-blue solution that contains unpaired electrons occupying cavities in the solvent. These 'metal-ammonia solutions' have a maximum absorption at $1500 \mathrm{~nm}$. Supposing that the absorption is due to the excitation of an electron in a spherical square well from its ground state to the next-higher state (see the preceding problem for information), what is the radius of the cavity?
Plain-text mathematical notation (without MathML)
When alkali metals dissolve in liquid ammonia, their atoms each lose an electron and give rise to a deep-blue solution that contains unpaired electrons occupying cavities in the solvent. These 'metal-ammonia solutions' have a maximum absorption at $1500 \mathrm{~nm}$. Supposing that the absorption is due to the excitation of an electron in a spherical square well from its ground state to the next-higher state (see the preceding problem for information), what is the radius of the cavity?
Original LaTeX notation
When alkali metals dissolve in liquid ammonia, their atoms each lose an electron and give rise to a deep-blue solution that contains unpaired electrons occupying cavities in the solvent. These 'metal-ammonia solutions' have a maximum absorption at $1500 \mathrm{~nm}$. Supposing that the absorption is due to the excitation of an electron in a spherical square well from its ground state to the next-higher state (see the preceding problem for information), what is the radius of the cavity?

category

chemistry

options

  1. 0.45 nm
  2. 0.89 $\mathrm{~nm}$
  3. 0.75 $\mathrm{~nm}$
  4. 0.69 $\mathrm{~nm}$
  5. 0.99 nm
  6. 1.25 nm
  7. 0.62 nm
  8. 0.30 nm
  9. 0.54 $\mathrm{~nm}$
  10. 1.10 nm

src

scibench-matter

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Source and history

upstream_id / Original problem ID
4353
task_id
7292777c-6f99-54da-8999-79a46fccc49f
task_key
default--test--4353
task_revision_id
1
config / split
default / test

Official source

initial import