ScienceShot science reference

Hydrogen and Rydberg spectrum

hydrogen_spectrum

Read-onlyIdempotent

Calculate reduced-mass Rydberg vacuum and standard-air wavelengths, level energies and ionization energies for H, D or a one-electron ion. Supply integer lower and upper levels; custom ions need Z and a bare nuclear mass in kg. Air uses Edlen (1966), dry air at 15 C and 101325 Pa, from 300 to 1700 nm; fine structure and Lamb shifts are excluded.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "n_lower": "<n_lower>",
      "n_upper": "<n_upper>"
    },
    "name": "hydrogen_spectrum"
  }
}

Input Schema

Name	Required	Description
`z`	No	Integer nuclear charge 1 to 20, required for ion.
`n_lower`	Yes	Lower principal quantum number, integer >= 1.
`n_upper`	Yes	Upper principal quantum number, integer > n_lower and <= 10000.
`species`	No	H, D or ion; default H.
`nuclear_mass_kg`	No	Bare nuclear mass in kg, required for ion.

Schema Changelog

Changes observed during successful MCP inspections.

First observedNov 7, 2026

TDQS

A4.7/5.0

Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Goes well beyond the annotations by disclosing the underlying model and its validity envelope: Edlen (1966) for air, dry air at 15 C and 101325 Pa, applicability from 300 to 1700 nm. It also flags what is deliberately omitted (fine structure and Lamb shifts), which tells the agent exactly when results will be approximate rather than exact.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Three tight sentences: capability first, required inputs second, model limitations last. Every clause carries information an agent needs, and nothing is repeated from the schema verbatim.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

There is no output schema, but the description names all returned quantities (wavelengths in two media, level energies, ionization energies), so the agent knows what to expect. Combined with the stated physical model limits and species coverage, nothing material is missing for correct invocation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3, but the description adds meaning by tying nuclear_mass_kg to the reduced-mass treatment and reinforcing that levels must be integers. The remaining parameter details are already carried by the schema, so no further credit is warranted.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

Opens with a specific verb ('Calculate') and the exact physical quantities returned (reduced-mass Rydberg vacuum and standard-air wavelengths, level energies, ionization energies), plus the supported species. This cleanly separates it from siblings like xray_spectrum or blackbody_spectrum, which cover different radiation domains.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives clear selection conditions for the species argument ('H, D or a one-electron ion') and states what custom ions require (Z plus a bare nuclear mass in kg). It stops short of explicit exclusions or naming a sibling tool when the user wants, e.g., X-ray transitions instead.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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